This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A010354 #31 Feb 16 2025 08:32:32
%S A010354 1,2,3,4,5,6,7,20,52,92,133,307,432,433,16819,17864,17865,24583,25639,
%T A010354 212419,906298,906426,938811,1122179,2087646,3821955,13606405,
%U A010354 40695508,423056951,637339524,6710775966,13892162580,32298119799,97095152738,98250308556,98317417420,125586038802
%N A010354 Base-8 Armstrong or narcissistic numbers (written in base 10).
%C A010354 Like the other single-digit terms, zero would satisfy the definition (n = Sum_{i=1..k} d[i]^k when d[1..k] are the base 8 digits of n), but here only positive numbers are considered. - _M. F. Hasler_, Nov 20 2019
%H A010354 Joseph Myers, <a href="/A010354/b010354.txt">Table of n, a(n) for n = 1..62</a> (the full list of terms, from Winter)
%H A010354 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NarcissisticNumber.html">Narcissistic Number</a>
%H A010354 D. T. Winter, <a href="http://ftp.cwi.nl/dik/Armstrong">Table of Armstrong Numbers</a>
%e A010354 From _M. F. Hasler_, Nov 20 2019: (Start)
%e A010354 20 = 24_8 (in base 8), and 2^2 + 4^2 = 20.
%e A010354 432 = 660_8, and 6^3 + 6^3 + 0^3 = 432; it's easy to see that 432 + 1 then also satisfies the equation, as for any term that is a multiple of 8. (End)
%o A010354 (PARI) select( {is_A010354(n)=n==vecsum([d^#n|d<-n=digits(n,8)])}, [0..10^6]) \\ This gives only terms < 10^6, for illustration of is_A010354(). - _M. F. Hasler_, Nov 20 2019
%o A010354 (Python)
%o A010354 from itertools import islice, combinations_with_replacement
%o A010354 def A010354_gen(): # generator of terms
%o A010354 for k in range(1,30):
%o A010354 a = tuple(i**k for i in range(8))
%o A010354 yield from (x[0] for x in sorted(filter(lambda x:x[0] > 0 and tuple(int(d,8) for d in sorted(oct(x[0])[2:])) == x[1], \
%o A010354 ((sum(map(lambda y:a[y],b)),b) for b in combinations_with_replacement(range(8),k)))))
%o A010354 A010354_list = list(islice(A010354_gen(),20)) # _Chai Wah Wu_, Apr 20 2022
%Y A010354 Cf. A010351 (a(n) written in base 8).
%Y A010354 In other bases: A010344 (base 4), A010346 (base 5), A010348 (base 6), A010350 (base 7), A010353 (base 9), A005188 (base 10), A161948 (base 11), A161949 (base 12), A161950 (base 13), A161951 (base 14), A161952 (base 15), A161953 (base 16).
%K A010354 base,fini,full,nonn
%O A010354 1,2
%A A010354 _N. J. A. Sloane_
%E A010354 Edited by _Joseph Myers_, Jun 28 2009