# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a161953 Showing 1-1 of 1 %I A161953 #34 Apr 21 2022 10:55:57 %S A161953 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,342,371,520,584,645,1189,1456, %T A161953 1457,1547,1611,2240,2241,2458,2729,2755,3240,3689,3744,3745,47314, %U A161953 79225,177922,177954,368764,369788,786656,786657,787680,787681,811239,812263,819424,819425,820448,820449,909360 %N A161953 Base-16 Armstrong or narcissistic numbers (written in base 10). %C A161953 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 %H A161953 Joseph Myers, Table of n, a(n) for n=1..293 (the full list of terms, from Winter) %H A161953 Henk Koppelaar and Peyman Nasehpour, On Hardy's Apology Numbers, arXiv:2008.08187 [math.NT], 2020. %H A161953 Eric Weisstein's World of Mathematics, Narcissistic Number %H A161953 D. T. Winter, Table of Armstrong Numbers %e A161953 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.) %t A161953 Select[Range[10^7], # == Total[IntegerDigits[#, 16]^IntegerLength[#, 16]] &] (* _Michael De Vlieger_, Nov 04 2020 *) %o A161953 (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 %o A161953 (PARI) select( is_A161953(n)={n==vecsum([d^#n|d<-n=digits(n,16)])}, [1..10^5]) \\ _M. F. Hasler_, Nov 22 2019 %o A161953 (Python) %o A161953 from itertools import islice, combinations_with_replacement %o A161953 def A161953_gen(): # generator of terms %o A161953 for k in range(1,74): %o A161953 a = tuple(i**k for i in range(16)) %o A161953 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], \ %o A161953 ((sum(map(lambda y:a[y],b)),b) for b in combinations_with_replacement(range(16),k))))) %o A161953 A161953_list = list(islice(A161953_gen(),30)) # _Chai Wah Wu_, Apr 21 2022 %Y A161953 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). %K A161953 base,fini,full,nonn %O A161953 1,2 %A A161953 _Joseph Myers_, Jun 22 2009 %E A161953 Terms sorted in increasing order by _Pontus von Brömssen_, Mar 03 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE