login
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.
11
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
KEYWORD
base,nonn
AUTHOR
Joseph Myers, Jun 28 2009
STATUS
approved