It seems that it grows quite slowly, probaby because there is no scarcity of multiples. If I'm not wrong S(100)=2790, S(1000)=13761, S(10000)= 27469. badQ[n_] := StringMatchQ[ToString@n, RegularExpression[".*70[^7]+7.*|.*77.*|[^7]+|^7.*|.*7$"]]; L = {170}; While[Length[L] < 1000, v = ToExpression[StringReplace[ToString[L[[-1]]], "7" -> "+"]]; k = v; While[badQ[k] || MemberQ[L, k], k += v]; AppendTo[L, k]]; L Giovanni Il 20/05/2020 19:45, Éric Angelini ha scritto:
Hello Math-Fun, The Seven+ operation transforms a digit 7 into a plus sign.
The integer 170 becomes 1+0 which is 1. We want that a(n), transformed by the Seven+ operation, divides a(n+1). The term a(n+1) has to contain at least one digit 7. No two identical terms in the sequence S – which should be the lexico-first of its kind.
For a(1) = 170, we get:
S = 170, 171, 172, 174, 175, 270, 176, 273, 275, 371, 272, 276, 376, 279, 374, 378, 473, 476, 370,...
We see indeed that: 170 = 1+0 = 1 divides 171; 171 = 1+1 = 2 divides 172; 172 = 1+2 = 3 divides 174; 174 = 1+4 = 5 divides 175; 175 = 1+5 = 6 divides 270; etc.
Numbers we don't want to see in S: — no term starting with a 7 (ex. 754 or 7574); — no term ending with a 7 (ex. 127 or 1727); — no term with 2 or more consecutive 7 (ex. 1778); — between two 7, no string with a leading 0 (ex. 170578 – but 17078 is ok as this term would produce 9).
Where does S (S for "seven") go? As usual, please forgive my hand mistakes. Best, É.
Nothing more on my personal web page: http://cinquantesignes.blogspot.com/2020/05/seven-plus.html
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun