A256359 Numbers n such that there is at least one base b in which n is a multiple-digit narcissistic number.
5, 8, 10, 13, 17, 18, 20, 25, 26, 28, 29, 32, 35, 37, 40, 41, 43, 45, 50, 52, 53, 55, 58, 61, 62, 65, 68, 72, 80, 82, 83, 85, 90, 92, 97, 98, 99, 101, 104, 109, 113, 117, 118, 122, 125, 126, 127, 128, 133, 134, 136, 145, 146, 148, 152, 153, 160, 162
Offset: 1
Examples
a(1) = 5 because this is the first number that is a multiple-digit narcissistic number in at least one base (3).
Links
- Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..53569
- W. Schneider, Perfect Digital Invariants: Pluperfect Digital Invariants(PPDIs)
- Eric Weisstein's World of Mathematics, Narcissistic Number
- Wikipedia, Narcissistic number
Crossrefs
Programs
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Mathematica
Select[Range@ 162, Function[k, AnyTrue[Range[2, k], Total[#^Length@ #] &@ IntegerDigits[k, #] == k &]]] (* Version 10, or *) Select[Range@ 162, Function[k, Total@ Boole[Total[#^Length@ #] &@ IntegerDigits[k, #] == k & /@ Range[2, k]] > 0]] (* Michael De Vlieger, Apr 30 2016 *)
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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,", ")))