

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 baseb expansion of m.


11



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
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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 (k2)/4 sequences.
It is not known if this sequence is infinite.
The eight terms 10 through 206 are all twice primes (cf. A349820).


LINKS

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


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

This is the limiting row of A350601.


KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



