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.

0, 1, 2, 6, 8, 10, 11, 12, 13, 14, 15, 17, 20, 21, 22, 24, 26, 27, 28, 29, 30, 31, 32, 35, 36, 37, 39, 40, 41, 42, 44, 46, 47, 50, 51, 52, 53, 55, 57, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 80, 81, 82, 83, 85, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97

Offset: 0

Author

Eric Angelini, May 29 2007

Keywords

• base
• easy
• nonn

Comments

Terms computed by Stefan Steinerberger.

Includes all numbers that end with 0 or 1. - Robert Israel, Feb 06 2025

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A375211.

Programs

Maple

f:= proc(n) local Ln, Lk,k;
  Ln:= convert(convert(n,base,10),set);
  for k from n+1 do
     Lk:= convert(convert(k,base,10),set) union Ln;
     if convert(convert(n*k,base,10),set) intersect Lk <> {} then return k fi
  od
end proc:
Res:= 0: x:= 0:
for i from 1 to 100 do x:= f(x); Res:= Res,x od:
Res; # Robert Israel, Feb 06 2025

Mathematica

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