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A010348 Base-6 Armstrong or narcissistic numbers (written in base 10). 15

%I #31 Nov 29 2019 20:31:13

%S 1,2,3,4,5,99,190,2292,2293,2324,3432,3433,6197,36140,269458,391907,

%T 10067135,2510142206,2511720147,3866632806,3866632807,3930544834,

%U 4953134588,5018649129,6170640875,124246559501,4595333541803,5341093125744,5341093125745,19418246235419

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

%C From _M. F. Hasler_, Nov 20 2019: (Start)

%C 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 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NarcissisticNumber.html">Narcissistic Number</a>

%H 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 (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 Cf. A010347 (a(n) written in base 6).

%Y 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 base,fini,full,nonn

%O 1,2

%A _N. J. A. Sloane_

%E Edited by _Joseph Myers_, Jun 28 2009

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)