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A161953
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Base-16 Armstrong or narcissistic numbers (written in base 10).
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14
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 342, 371, 520, 584, 645, 1189, 1456, 1457, 1547, 1611, 2240, 2241, 2458, 2729, 2755, 3240, 3689, 3744, 3745, 47314, 79225, 177922, 177954, 368764, 369788, 786656, 786657, 787680, 787681, 811239, 812263, 819424, 819425, 820448, 820449, 909360
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OFFSET
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1,2
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COMMENTS
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Whenever 16|a(n) (n = 22, 26, 33, 41, 43, 47, 49, 51, 53, 61, 116, 149, 157, 196, 198, 204, 206, 243, 247), then a(n+1) = a(n) + 1. Zero also satisfies the definition (n = Sum_{i=1..k} d[i]^k where d[1..k] are the base-16 digits of n), but this sequence only considers positive terms. - M. F. Hasler, Nov 22 2019
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LINKS
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EXAMPLE
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645 is in the sequence because 645 is 285 in hexadecimal and 2^3 + 8^3 + 5^3 = 645. (The exponent 3 is the number of hexadecimal digits.)
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MATHEMATICA
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Select[Range[10^7], # == Total[IntegerDigits[#, 16]^IntegerLength[#, 16]] &] (* Michael De Vlieger, Nov 04 2020 *)
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PROG
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(PARI) isok(n) = {my(b=16, d=digits(n, b), e=#d); sum(k=1, #d, d[k]^e) == n; } \\ Michel Marcus, Feb 25 2019
(PARI) select( is_A161953(n)={n==vecsum([d^#n|d<-n=digits(n, 16)])}, [1..10^5]) \\ M. F. Hasler, Nov 22 2019
(Python)
from itertools import islice, combinations_with_replacement
def A161953_gen(): # generator of terms
for k in range(1, 74):
a = tuple(i**k for i in range(16))
yield from (x[0] for x in sorted(filter(lambda x:x[0] > 0 and tuple(int(d, 16) for d in sorted(hex(x[0])[2:])) == x[1], \
((sum(map(lambda y:a[y], b)), b) for b in combinations_with_replacement(range(16), k)))))
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CROSSREFS
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In other bases: A010344 (base 4), A010346 (base 5), A010348 (base 6), A010350 (base 7), A010354 (base 8), A010353 (base 9), A005188 (base 10), A161948 (base 11), A161949 (base 12), A161950 (base 13), A161951 (base 14), A161952 (base 15).
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KEYWORD
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base,fini,full,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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