A070255 Numbers which divided into two substrings by breaking at any digit then one of them divides the other (0 is not to be considered a substring, multiples of 10 are excluded).

11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 26, 28, 31, 33, 36, 39, 41, 42, 44, 48, 51, 55, 61, 62, 63, 66, 71, 77, 81, 82, 84, 88, 91, 93, 99, 101, 102, 105, 111, 121, 122, 123, 124, 126, 131, 141, 142, 147, 151, 153, 155, 161, 162, 164, 168, 171, 181, 182, 183, 186

Offset

1,1

Comments

Conjecture: sequence is finite.

The conjecture above is false as terms of the form d00...00d, where d goes from 1 to 9, are always in the sequence. - FUNG Cheok Yin, Aug 12 2021

Links

FUNG Cheok Yin, Table of n, a(n) for n = 1..1000

Example

168 is a member as the possible substring partitions are (1,68 ) and (16,8). 1 divides 68 and 8 divides 16. 111111 is also a member with substring partitions (1,11111),(11,1111),(111,111),(1111,11),(11111,1). 1111111 is not a member as in the sub string partition (111,1111) 111 does not divide 1111.

Crossrefs

Sequence in context: A359983 A236403 A293728 * A267085 A284062 A261020

Adjacent sequences: A070252 A070253 A070254 * A070256 A070257 A070258

Keyword

base,nonn

Author

Amarnath Murthy, May 06 2002

Extensions

Corrected by T. D. Noe, Oct 25 2006

Missing terms 33 and 153 added by FUNG Cheok Yin, Aug 12 2021

Status

approved