A162219 Base 4 perfect digital invariants (written in base 10): numbers equal to the sum of the k-th powers of their base-4 digits, for some k.

0, 1, 2, 3, 8, 9, 28, 29, 32, 33, 35, 43, 55, 62, 83, 128, 129, 243, 512, 513, 922, 2048, 2049, 2316, 2317, 2444, 2445, 2571, 2699, 7330, 8192, 8193, 13124, 13125, 20710, 21222, 32768, 32769, 40392, 40393, 131072, 131073, 524288, 524289, 1075174

Offset

1,3

Comments

Whenever a(n) is a multiple of 4, then a(n+1) = a(n) + 1 is also a base 4 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..6778 (complete to 1500 base 4 digits)

Prog

(PARI) select( {is_A162219(n, b=4)=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. A162220 (corresponding exponents), A010344 (restriction to power = number of digits), A033836, A162221. In other bases: A162216 (base 3), A162222 (base 5), A162225 (base 6), A162228 (base 7), A162231 (base 8), A162234 (base 9), A023052 (base 10).

Sequence in context: A271394 A030439 A119386 * A140484 A087034 A364382

Adjacent sequences: A162216 A162217 A162218 * A162220 A162221 A162222

Keyword

base,nonn

Author

Joseph Myers, Jun 28 2009

Status

approved