[math-fun] A046693 -- A famous hard sequence (graceful graphs, sparse rulers) has a very elegant pattern
A046693 Size of smallest subset S of N={0,1,2,...,n} such that S-S=N, where S-S={abs(i-j) | i,j in S}. Also minimal marks for a sparse ruler of length n.Also minimal vertices in a graceful graph with n edges. Here are the first 11999 values of A046693 - round(sqrt(3*n+9/4)) 00 000 000 000 00000 00000 00000 0000000 0000000 0000000 000100000 001000000 000100000 00000000000 00000000000 00000000000 0000010000000 0001100000000 0110010000000 001110000000000 001110000000000 001110000000000 00011001000000000 11100110000000000 10011001000000000 0111111000000000000 1111111000000000000 0111111000000000000 111001100100000000000 111110011000000000000 111001100100000000000 10011111100000000000000 11111111100000000000000 10011111100000000000000 1111100110010000000000000 1111111001100000000000000 1111100110010000000000000 111001111110000000000000000 011111111110000000000000000 111001111110000000000000000 11111110011001000000000000000 11111111100110000000000000000 11111110011001000000000000000 1111100111111000000000000000000 1001111111111000000000000000000 1111100111111000000000000000000 111111111001100100000000000000000 111111111110011000000000000000000 111111111001100100000000000000000 01111110011111100000000000000000000 11100111111111100000000000000000000 01111110011111100000000000000000000 1111111111100110010000000000000000000 1111111111111001100000000000000000000 1111111111100110010000000000000000000 100111111001111110000000000000000000000 111110011111111110000000000000000000000 100111111001111110000000000000000000000 Does anyone else see the pattern? --Ed Pegg Jr
Maybe this will work. 00 000 000 000 00000 00000 00000 0000000 0000000 0000000 000100000 001000000 000100000 00000000000 00000000000 00000000000 0000010000000 0001100000000 0110010000000 001110000000000 001110000000000 001110000000000 00011001000000000 11100110000000000 10011001000000000 0111111000000000000 1111111000000000000 0111111000000000000 111001100100000000000 111110011000000000000 111001100100000000000 10011111100000000000000 11111111100000000000000 10011111100000000000000 1111100110010000000000000 1111111001100000000000000 1111100110010000000000000 111001111110000000000000000 011111111110000000000000000 111001111110000000000000000 11111110011001000000000000000 11111111100110000000000000000 11111110011001000000000000000 1111100111111000000000000000000 1001111111111000000000000000000 1111100111111000000000000000000 111111111001100100000000000000000 111111111110011000000000000000000 111111111001100100000000000000000 01111110011111100000000000000000000 11100111111111100000000000000000000 01111110011111100000000000000000000 1111111111100110010000000000000000000 1111111111111001100000000000000000000 1111111111100110010000000000000000000 100111111001111110000000000000000000000 111110011111111110000000000000000000000 100111111001111110000000000000000000000 On Wednesday, July 17, 2019, 10:36:21 AM CDT, ed pegg <ed@mathpuzzle.com> wrote: A046693 Size of smallest subset S of N={0,1,2,...,n} such that S-S=N, where S-S={abs(i-j) | i,j in S}. Also minimal marks for a sparse ruler of length n.Also minimal vertices in a graceful graph with n edges. Here are the first 11999 values of A046693 - round(sqrt(3*n+9/4)) 00 000 000 000 00000 00000 00000 0000000 0000000 0000000 000100000 001000000 000100000 00000000000 00000000000 00000000000 0000010000000 0001100000000 0110010000000 001110000000000 001110000000000 001110000000000 00011001000000000 11100110000000000 10011001000000000 0111111000000000000 1111111000000000000 0111111000000000000 111001100100000000000 111110011000000000000 111001100100000000000 10011111100000000000000 11111111100000000000000 10011111100000000000000 1111100110010000000000000 1111111001100000000000000 1111100110010000000000000 111001111110000000000000000 011111111110000000000000000 111001111110000000000000000 11111110011001000000000000000 11111111100110000000000000000 11111110011001000000000000000 1111100111111000000000000000000 1001111111111000000000000000000 1111100111111000000000000000000 111111111001100100000000000000000 111111111110011000000000000000000 111111111001100100000000000000000 01111110011111100000000000000000000 11100111111111100000000000000000000 01111110011111100000000000000000000 1111111111100110010000000000000000000 1111111111111001100000000000000000000 1111111111100110010000000000000000000 100111111001111110000000000000000000000 111110011111111110000000000000000000000 100111111001111110000000000000000000000 Does anyone else see the pattern? --Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Will the line returns work now? 00 000 000 000 00000 00000 00000 0000000 0000000 0000000 000100000 001000000 000100000 00000000000 00000000000 00000000000 0000010000000 0001100000000 0110010000000 001110000000000 001110000000000 001110000000000 00011001000000000 11100110000000000 10011001000000000 0111111000000000000 1111111000000000000 0111111000000000000 111001100100000000000 111110011000000000000 111001100100000000000 10011111100000000000000 11111111100000000000000 10011111100000000000000 1111100110010000000000000 1111111001100000000000000 1111100110010000000000000 111001111110000000000000000 011111111110000000000000000 111001111110000000000000000 11111110011001000000000000000 11111111100110000000000000000 11111110011001000000000000000 1111100111111000000000000000000 1001111111111000000000000000000 1111100111111000000000000000000 111111111001100100000000000000000 111111111110011000000000000000000 111111111001100100000000000000000 01111110011111100000000000000000000 11100111111111100000000000000000000 01111110011111100000000000000000000 1111111111100110010000000000000000000 1111111111111001100000000000000000000 1111111111100110010000000000000000000 100111111001111110000000000000000000000 111110011111111110000000000000000000000 100111111001111110000000000000000000000 On Wednesday, July 17, 2019, 10:42:29 AM CDT, ed pegg <ed@mathpuzzle.com> wrote: Maybe this will work. 00 000 000 000 00000 00000 00000 0000000 0000000 0000000 000100000 001000000 000100000 00000000000 00000000000 00000000000 0000010000000 0001100000000 0110010000000 001110000000000 001110000000000 001110000000000 00011001000000000 11100110000000000 10011001000000000 0111111000000000000 1111111000000000000 0111111000000000000 111001100100000000000 111110011000000000000 111001100100000000000 10011111100000000000000 11111111100000000000000 10011111100000000000000 1111100110010000000000000 1111111001100000000000000 1111100110010000000000000 111001111110000000000000000 011111111110000000000000000 111001111110000000000000000 11111110011001000000000000000 11111111100110000000000000000 11111110011001000000000000000 1111100111111000000000000000000 1001111111111000000000000000000 1111100111111000000000000000000 111111111001100100000000000000000 111111111110011000000000000000000 111111111001100100000000000000000 01111110011111100000000000000000000 11100111111111100000000000000000000 01111110011111100000000000000000000 1111111111100110010000000000000000000 1111111111111001100000000000000000000 1111111111100110010000000000000000000 100111111001111110000000000000000000000 111110011111111110000000000000000000000 100111111001111110000000000000000000000 On Wednesday, July 17, 2019, 10:36:21 AM CDT, ed pegg <ed@mathpuzzle.com> wrote: A046693 Size of smallest subset S of N={0,1,2,...,n} such that S-S=N, where S-S={abs(i-j) | i,j in S}. Also minimal marks for a sparse ruler of length n.Also minimal vertices in a graceful graph with n edges. Here are the first 11999 values of A046693 - round(sqrt(3*n+9/4)) 00 000 000 000 00000 00000 00000 0000000 0000000 0000000 000100000 001000000 000100000 00000000000 00000000000 00000000000 0000010000000 0001100000000 0110010000000 001110000000000 001110000000000 001110000000000 00011001000000000 11100110000000000 10011001000000000 0111111000000000000 1111111000000000000 0111111000000000000 111001100100000000000 111110011000000000000 111001100100000000000 10011111100000000000000 11111111100000000000000 10011111100000000000000 1111100110010000000000000 1111111001100000000000000 1111100110010000000000000 111001111110000000000000000 011111111110000000000000000 111001111110000000000000000 11111110011001000000000000000 11111111100110000000000000000 11111110011001000000000000000 1111100111111000000000000000000 1001111111111000000000000000000 1111100111111000000000000000000 111111111001100100000000000000000 111111111110011000000000000000000 111111111001100100000000000000000 01111110011111100000000000000000000 11100111111111100000000000000000000 01111110011111100000000000000000000 1111111111100110010000000000000000000 1111111111111001100000000000000000000 1111111111100110010000000000000000000 100111111001111110000000000000000000000 111110011111111110000000000000000000000 100111111001111110000000000000000000000 Does anyone else see the pattern? --Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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ed pegg