A230624 Numbers k with property that for every base b >= 2, there is a number m such that m+s(m) = k, where s(m) = sum of digits in the base-b expansion of m.

0, 2, 10, 14, 22, 38, 62, 94, 158, 206, 318, 382, 478, 606, 766, 958, 1022, 1534, 1662, 1726, 1790, 1918, 1982, 2238, 2622, 2686, 3006, 3262, 3582, 3966, 4734, 5118, 5374, 5758, 5886, 6782, 8830, 9342, 9470, 9598, 10878, 12926, 13182, 13438, 14718, 18686, 22526

Offset

1,2

Comments

If k is a positive term then k is even (or else k has no generator in base k+1) but not a multiple of 4 (or else k has no generator in base k/2). - David Applegate, Jan 09 2022. See A349821 and A350607 for the k/2 and (k-2)/4 sequences.

It is not known if this sequence is infinite.

The eight terms 10 through 206 are all twice primes (cf. A349820).

Links

David Applegate, Table of n, a(n) for n = 1..547, terms < 10^9 (first 90 terms from Lars Blomberg)

David Applegate, Two graphs to accompany Comments (see next link)

David Applegate and N. J. A. Sloane, Comments on A230624, Numbers that are generated in every base

Santanu Bandyopadhyay, Self-Number, Indian Institute of Technology Bombay (Mumbai, India, 2020).

Santanu Bandyopadhyay, Self-Number, Indian Institute of Technology Bombay (Mumbai, India, 2020). [Local copy]

Cai, Tianxin, On k-self-numbers and universal generated numbers, Fibonacci Quart. 34 (1996), no. 2, 144--146. MR1386983 (97c:11008)

Index entries for Colombian or self numbers and related sequences

Example

10 is a member because in base 2, 7=111, 7+3=10; in base 3, 7=21, 7+3=10; in base 4, 8=20, 8+2=10; in base 5, 7=12, 7+3=10; and in bases b >= 6, 5+5=10.

Crossrefs

Cf. A003052, A349820, A349821, A349822, A350607.

For first differences see A349823.

This is the limiting row of A350601.

Sequence in context: A350059 A349833 A091999 * A290143 A160773 A217191

Adjacent sequences: A230621 A230622 A230623 * A230625 A230626 A230627

Keyword

nonn,base

Author

N. J. A. Sloane, Oct 27 2013

Extensions

More terms from Lars Blomberg, Oct 12 2015

More terms from David Applegate, Jan 02 2022

Status

approved