A161951 - OEIS

%I #30 Feb 16 2025 08:33:10

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,244,793,282007,10362564,1445712420,

%T 29546248981,164159496751,342515735622,359057049845,216210334578515,

%U 324075236456868,338527182572746,338609726265795,382789516519507,435198066019184,526088332647250

%N Base-14 Armstrong or narcissistic numbers (written in base 10).

%C Whenever 14|a(n) (n = 36, 46, 75, 77), 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-14 digits of n), but this sequence only considers positive terms. - _M. F. Hasler_, Nov 22 2019

%H Joseph Myers, <a href="/A161951/b161951.txt">Table of n, a(n) for n=1..103</a> (the full list of terms, from Winter)

%H Henk Koppelaar and Peyman Nasehpour, <a href="https://arxiv.org/abs/2008.08187">On Hardy's Apology Numbers</a>, arXiv:2008.08187 [math.NT], 2020.

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

%H D. T. Winter, <a href="https://deimel.org/rec_math/dik2.htm">Table of Armstrong Numbers</a>

%t Select[Range[2 * 10^7], # == Total[IntegerDigits[#, 14]^IntegerLength[#, 14]] &] (* _Michael De Vlieger_, Nov 04 2020 *)

%o (PARI) select( is_A161951(n)={n==vecsum([d^#n|d<-n=digits(n,14)])}, [1..10^6\3]) \\ _M. F. Hasler_, Nov 22 2019

%Y 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), A161952 (base 15), A161953 (base 16).

%K base,fini,full,nonn

%O 1,2

%A _Joseph Myers_, Jun 22 2009