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A161953
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Base-16 Armstrong or narcissistic numbers (written in base 10).
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13
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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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refs;
listen;
history;
text;
internal format)
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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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Joseph Myers, Table of n, a(n) for n=1..293 (the full list of terms, from Winter)
Henk Koppelaar and Peyman Nasehpour, On Hardy's Apology Numbers, arXiv:2008.08187 [math.NT], 2020.
Eric Weisstein's World of Mathematics, Narcissistic Number
D. T. Winter, Table of Armstrong Numbers
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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
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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).
Sequence in context: A043320 A044917 A246337 * A187829 A105427 A247160
Adjacent sequences: A161950 A161951 A161952 * A161954 A161955 A161956
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KEYWORD
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base,fini,full,nonn
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AUTHOR
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Joseph Myers, Jun 22 2009
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EXTENSIONS
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Terms sorted in increasing order by Pontus von Brömssen, Mar 03 2019
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STATUS
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approved
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