cp's OEIS Frontend

A010348 Base-6 Armstrong or narcissistic numbers (written in base 10).

%I A010348 #32 Feb 16 2025 08:32:32
%S A010348 1,2,3,4,5,99,190,2292,2293,2324,3432,3433,6197,36140,269458,391907,
%T A010348 10067135,2510142206,2511720147,3866632806,3866632807,3930544834,
%U A010348 4953134588,5018649129,6170640875,124246559501,4595333541803,5341093125744,5341093125745,19418246235419
%N A010348 Base-6 Armstrong or narcissistic numbers (written in base 10).
%C A010348 From _M. F. Hasler_, Nov 20 2019: (Start)
%C A010348 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 digits of n), but here only positive numbers are considered.
%C A010348 Terms a(n+1) = a(n) + 1 (n = 8, 11, 20, 28) correspond to solutions a(n) ending in a digit 0 in base 6, in which case a(n) + 1 also is a solution. (End)
%H A010348 Joseph Myers, <a href="/A010348/b010348.txt">Table of n, a(n) for n = 1..30</a> (the full list of terms, from Winter)
%H A010348 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NarcissisticNumber.html">Narcissistic Number</a>
%H A010348 D. T. Winter, <a href="http://web.archive.org/web/20100109234250/http://ftp.cwi.nl:80/dik/Armstrong">Table of Armstrong Numbers</a> (latest backup on web.archive.org from Jan. 2010; page no longer available), published not later than Aug. 2003.
%o A010348 (PARI) select( {is_A010348(n)=n==vecsum([d^#n|d<-n=digits(n,6)])}, [0..4e5\1]) \\ Note: this yields only terms < 10^6, for illustration of is_A010348(). - _M. F. Hasler_, Nov 20 2019
%Y A010348 Cf. A010347 (a(n) written in base 6).
%Y A010348 In other bases: A010344 (base 4), A010346 (base 5), 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), A161953 (base 16).
%K A010348 base,fini,full,nonn
%O A010348 1,2
%A A010348 _N. J. A. Sloane_
%E A010348 Edited by _Joseph Myers_, Jun 28 2009