A162222 Base 5 perfect digital invariants (written in base 10): numbers equal to the sum of the k-th powers of their base-5 digits, for some k.

0, 1, 2, 3, 4, 13, 18, 28, 118, 257, 289, 308, 353, 419, 4890, 4891, 9113, 16387, 66562, 322217, 1874374, 172449032, 268533762, 338749352, 2204944815, 2204944816, 2415951874, 3250054360, 3250054361, 3264337734, 4424304070, 4424304071

Offset

1,3

Comments

Whenever a(n) is a multiple of 5, then a(n+1) = a(n) + 1 is also a base 5 perfect digital invariant, with the same exponent k. - M. F. Hasler, Nov 21 2019

Links

Joseph Myers, Table of n, a(n) for n=1..1640 (complete to 700 base 5 digits)

Prog

(PARI) select( {is_A162222(n, b=5)=n<b||forstep(k=logint(n, max(vecmax(b=digits(n, b)), 2)), 2, -1, my(t=vecsum([d^k|d<-b])); t>n||return(t==n))}, [0..10^5]) \\ M. F. Hasler, Nov 21 2019

Crossrefs

Cf. A162223 (corresponding exponents), A010346 (restriction to power = number of digits), A033837, A162224. In other bases: A162216 (base 3), A162219 (base 4), A162225 (base 6), A162228 (base 7), A162231 (base 8), A162234 (base 9), A023052 (base 10).

Sequence in context: A295396 A236440 A357954 * A010346 A295621 A295755

Adjacent sequences: A162219 A162220 A162221 * A162223 A162224 A162225

Keyword

base,nonn

Author

Joseph Myers, Jun 28 2009

Status

approved