[math-fun] Digitsum and Digitroot
Hello Math-Fun, are 29, 38, 47, 48 and 49 the first five integers whose digitroot is NOT a substring of the digitsum? Best, É. Catapulté de mon aPhone
You missed 39. The numbers up to 100 with digital root not a substring of their digit sum are (first column is the number, second is the digital root, third is the digit sum): 29 2 11 38 2 11 39 3 12 47 2 11 48 3 12 49 4 13 56 2 11 57 3 12 58 4 13 59 5 14 65 2 11 66 3 12 67 4 13 68 5 14 69 6 15 74 2 11 75 3 12 76 4 13 77 5 14 78 6 15 79 7 16 83 2 11 84 3 12 85 4 13 86 5 14 87 6 15 88 7 16 89 8 17 92 2 11 93 3 12 94 4 13 95 5 14 96 6 15 97 7 16 98 8 17 99 9 18 On Fri, Feb 28, 2020 at 10:31 AM Éric Angelini <eric.angelini@skynet.be> wrote:
Hello Math-Fun, are 29, 38, 47, 48 and 49 the first five integers whose digitroot is NOT a substring of the digitsum? Best, É. Catapulté de mon aPhone
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Yes indeed Tom, many thanks ! Best, É. Catapulté de mon aPhone
Le 28 févr. 2020 à 20:25, Tom Duff <td@pixar.com> a écrit :
You missed 39. The numbers up to 100 with digital root not a substring of their digit sum are (first column is the number, second is the digital root, third is the digit sum): 29 2 11 38 2 11 39 3 12 47 2 11 48 3 12 49 4 13 56 2 11 57 3 12 58 4 13 59 5 14 65 2 11 66 3 12 67 4 13 68 5 14 69 6 15 74 2 11 75 3 12 76 4 13 77 5 14 78 6 15 79 7 16 83 2 11 84 3 12 85 4 13 86 5 14 87 6 15 88 7 16 89 8 17 92 2 11 93 3 12 94 4 13 95 5 14 96 6 15 97 7 16 98 8 17 99 9 18
On Fri, Feb 28, 2020 at 10:31 AM Éric Angelini <eric.angelini@skynet.be> wrote:
Hello Math-Fun, are 29, 38, 47, 48 and 49 the first five integers whose digitroot is NOT a substring of the digitsum? Best, É. Catapulté de mon aPhone
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Hello Math-Fun, please have a look here, this is math-fun, I guess, though I have a few worries (in yellow color): http://cinquantesignes.blogspot.com/2020/03/substrings-so-far.html This page starts like this: “Describe my substrings so far” Definition: a(n) is the count of substrings a(n+1) so far in the sequence, including a(n+1) itself. S = 1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,11,1,13,1,15,1,17,1,19,1,21,1,22,1,23,1,24,1,25,1,26,1,27,1,28,1,29,1,31,1,32,1,33,1,34,1,35,1,36,1,37,1,38,1,39,1,41,1,42,1,43,1,44,1,45,1,46,1,47,1,48,1,49,1,51,1,52,1,53,1,54,1,55,1,56,1,57,1,58,1,59,1,61,1,62,1,63,1,64,1,65,1,66,1,67,1,68,1,69,1,71,1,72,1,73,1,74,1,75,1,76,1,77,1,78,1,79,1,81,1,82,1,83,1,84,1,85,1,86,1,87,1,88,1,89,1,91,1,92,1,93,1,94,1,95,1,96,1,97,1,98,1,101,1,103,1,105,1,107,1,109,1,112,1,115,1,118,1,120,1,122,1,124,1,126,1,… S must be “read” like this, term by term from the left to the right: a(1) – there is 1 substring “2” so far in S; (true, if you consider the segment <1,2>); a(2) – there are 2 substrings “1” so far in S; (true, if you consider the segment <1,2,1>); a(3) – there is 1 substring “3” so far in S; (true, if you consider the segment <1,2,1,3>); a(4) – there are 3 substrings “1” so far in S; (true, if you consider the segment <1,2,1,3,1>); a(5) – there is 1 substring “4” so far in S; (true, if you consider the segment <1,2,1,3,1,4>); … a(14) – there are 8 substrings “1” so far in S; (true, if you consider the segment <1,2,1,3,1,4,1,5,1,6,1,7,1,8,1>); a(15) – there is 1 substring “11” so far in S; (true, if you consider the segment <1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,11>); a(16) – there are 11 substrings “1” so far in S; (true, if you consider the segment <1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,11,1>); Etc. Here are my worries: (...)
participants (3)
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Tom Duff -
Éric Angelini -
Éric Angelini