A162228 Base 7 perfect digital invariants (written in base 10): numbers equal to the sum of the k-th powers of their base-7 digits, for some k.

0, 1, 2, 3, 4, 5, 6, 9, 10, 16, 25, 32, 45, 65, 133, 134, 152, 250, 1542, 3190, 3222, 3612, 3613, 4183, 9286, 35411, 37271, 72865, 191334, 193393, 376889, 535069, 794376, 1110699, 2236488, 3021897, 4431562, 8094840, 9885773, 10883814, 16219922

Offset

1,3

Comments

Whenever a(n) is a multiple of 7, then a(n+1) = a(n) + 1 is also a base 7 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..868 (complete to 200 base 7 digits)

Prog

(PARI) select( {is_A162228(n, b=7)=n<b||forstep(k=logint(n, max(vecmax(b=digits(n, b)), 2)), 2, -1, my(s=vecsum([d^k|d<-b])); s>n||return(s==n))}, [0..10^5]) \\ M. F. Hasler, Nov 21 2019

Crossrefs

Cf. A162229 (corresponding exponents), A010350 (restriction to power = number of digits), A033839, A162230. In other bases: A162216 (base 3), A162219 (base 4), A162222 (base 5), A162225 (base 6), A162231 (base 8), A162234 (base 9), A023052 (base 10).

Sequence in context: A153013 A052492 A339454 * A085714 A240093 A286421

Adjacent sequences: A162225 A162226 A162227 * A162229 A162230 A162231

Keyword

base,nonn

Author

Joseph Myers, Jun 28 2009

Status

approved