A308479 Least k such that k*n and (k+1)*n fail to have a common nonzero digit, or 0 if this property never occurs.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 3, 1, 1, 1, 1, 2, 1, 1, 4, 1, 1, 2, 3, 1, 1, 1, 1, 1, 8, 1, 1, 2, 1, 1, 3, 1, 11, 1, 21, 1, 1, 1, 2, 5, 3, 5, 0, 1, 1, 2, 1, 1, 3

Offset

1,12

Comments

a(n) = 0 for the members of A308466.

Links

David Radcliffe, Table of n, a(n) for n = 1..10000

David Radcliffe, Python script for A308479

Formula

If a(n) = k, then a(10*n) = k.

Example

a(3) = 1 since 1*3 and 2*3 have no digit in common;
a(12) = 2 since 1*12 and 2*12 have the digit 2 in common, but 2*12 and 3*12 have no nonzero digit in common, thus a(12) = 2;
a(25) = 3 since 1*25 and 2*25 have the digit 5 in common, 2*25 and 3*25 have the digit 5 in common, but 3*25 and 4*25 have no nonzero digit in common; etc.

Mathematica

a = Compile[{{n, _Integer}}, Module[{k = 1, id1 = DeleteCases[ IntegerDigits[ n], 0], id2 = DeleteCases[ IntegerDigits[ 2n], 0]}, While[k < 1001 && Intersection[id1, id2] != {}, id1 = id2; k++; id2 = DeleteCases[ Union[ IntegerDigits[(k + 1) n]], 0]]; If[k == 1001, 0, k]]]; Array[a, 198]

Crossrefs

Cf. A308466.

Sequence in context: A330751 A327407 A290104 * A031280 A134870 A031286

Adjacent sequences: A308476 A308477 A308478 * A308480 A308481 A308482

Keyword

nonn,base

Author

David Radcliffe, Daniel Griller, and Robert G. Wilson v, May 29 2019

Status

approved