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A129459 Slowest increasing sequence that starts with 0 and has property that multiplying two consecutive terms gives a number which shares at least one digit with at least one of the terms.

%I A129459 #12 Feb 07 2025 00:32:56
%S A129459 0,1,2,6,8,10,11,12,13,14,15,17,20,21,22,24,26,27,28,29,30,31,32,35,
%T A129459 36,37,39,40,41,42,44,46,47,50,51,52,53,55,57,60,61,62,63,64,65,67,68,
%U A129459 69,70,71,72,73,74,75,76,78,80,81,82,83,85,87,88,89,90,91,92,94,95,96,97
%N A129459 Slowest increasing sequence that starts with 0 and has property that multiplying two consecutive terms gives a number which shares at least one digit with at least one of the terms.
%C A129459 Terms computed by _Stefan Steinerberger_.
%C A129459 Includes all numbers that end with 0 or 1. - _Robert Israel_, Feb 06 2025
%H A129459 Robert Israel, <a href="/A129459/b129459.txt">Table of n, a(n) for n = 0..10000</a>
%p A129459 f:= proc(n) local Ln, Lk,k;
%p A129459   Ln:= convert(convert(n,base,10),set);
%p A129459   for k from n+1 do
%p A129459      Lk:= convert(convert(k,base,10),set) union Ln;
%p A129459      if convert(convert(n*k,base,10),set) intersect Lk <> {} then return k fi
%p A129459   od
%p A129459 end proc:
%p A129459 Res:= 0: x:= 0:
%p A129459 for i from 1 to 100 do x:= f(x); Res:= Res,x od:
%p A129459 Res; # _Robert Israel_, Feb 06 2025
%t A129459 a = {0}; For[n = 1, n <= 100, n++, If[Length[Intersection[IntegerDigits[n*a[[ -1]]], Union[IntegerDigits[n], IntegerDigits[a[[ -1]]]]]] != 0, AppendTo[a, n]]]; a
%Y A129459 Cf. A375211.
%K A129459 base,easy,nonn
%O A129459 0,3
%A A129459 _Eric Angelini_, May 29 2007