A162231 Base 8 perfect digital invariants (written in base 10): numbers equal to the sum of the k-th powers of their base-8 digits, for some k.

0, 1, 2, 3, 4, 5, 6, 7, 16, 17, 20, 52, 92, 128, 129, 133, 256, 257, 272, 273, 307, 432, 433, 1024, 1025, 1056, 1057, 2323, 8192, 8193, 13379, 16384, 16385, 16512, 16513, 16819, 17864, 17865, 24583, 25639, 65536, 65537, 65792, 65793, 212419, 524288, 524289

Offset

1,3

Comments

Whenever a(n) is a multiple of 8, then a(n+1) = a(n) + 1 is also a base 8 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..1130 (complete to 160 base 8 digits)

Prog

(PARI) select( is_A162231(n, b=8)={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. A162232 (corresponding exponents), A010354 (restriction to power = number of digits), A033840, A162233. In other bases: A162216 (base 3), A162219 (base 4), A162222 (base 5), A162225 (base 6), A162228 (base 7), A162234 (base 9), A023052 (base 10).

Sequence in context: A371289 A004836 A039030 * A370957 A250045 A132028

Adjacent sequences: A162228 A162229 A162230 * A162232 A162233 A162234

Keyword

base,nonn

Author

Joseph Myers, Jun 28 2009

Status

approved