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

0,3

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

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

Crossrefs

Cf. A375211.

Sequence in context: A192125 A362666 A166270 * A028772 A325463 A121744

Adjacent sequences: A129456 A129457 A129458 * A129460 A129461 A129462

Keyword

base,easy,nonn

Author

Eric Angelini, May 29 2007

Status

approved