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A256359 Numbers n such that there is at least one base b in which n is a multiple-digit narcissistic number.

%I A256359 #28 Feb 16 2025 08:33:25
%S A256359 5,8,10,13,17,18,20,25,26,28,29,32,35,37,40,41,43,45,50,52,53,55,58,
%T A256359 61,62,65,68,72,80,82,83,85,90,92,97,98,99,101,104,109,113,117,118,
%U A256359 122,125,126,127,128,133,134,136,145,146,148,152,153,160,162
%N A256359 Numbers n such that there is at least one base b in which n is a multiple-digit narcissistic number.
%H A256359 Tim Johannes Ohrtmann, <a href="/A256359/b256359.txt">Table of n, a(n) for n = 1..53569</a>
%H A256359 W. Schneider, <a href="http://web.archive.org/web/20050213060737/http://www.wschnei.de/digit-related-numbers/pdi.html">Perfect Digital Invariants: Pluperfect Digital Invariants(PPDIs)</a>
%H A256359 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NarcissisticNumber.html">Narcissistic Number</a>
%H A256359 Wikipedia, <a href="http://en.wikipedia.org/wiki/Narcissistic_number">Narcissistic number</a>
%e A256359 a(1) = 5 because this is the first number that is a multiple-digit narcissistic number in at least one base (3).
%t A256359 Select[Range@ 162, Function[k, AnyTrue[Range[2, k], Total[#^Length@ #] &@ IntegerDigits[k, #] == k &]]] (* Version 10, or *)
%t A256359 Select[Range@ 162, Function[k, Total@ Boole[Total[#^Length@ #] &@ IntegerDigits[k, #] == k & /@ Range[2, k]] > 0]] (* _Michael De Vlieger_, Apr 30 2016 *)
%o A256359 (PARI) for(n=3,1000000, k=0; for(z=2,n, y=n; j=0; L=List(); until(y==0, x=y%z; j++; listinsert(L,x,j); while(!((y%z)==0), y--); y=y/z); t=0; for(p=1,j, t+=L[p]^j); if(n==t, k++)); if(k>0, print1(n,", ")))
%Y A256359 Cf. A005188.
%Y A256359 Cf. A256360, A256361, A256362, A256363, A256364, A256365 (1 to 6 bases).
%Y A256359 Cf. A256459 (first occurrences).
%K A256359 nonn,base
%O A256359 1,1
%A A256359 _Tim Johannes Ohrtmann_, Mar 26 2015