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