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

1,1

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

Example

a(1) = 5 because this is the first number that is a multiple-digit narcissistic number in at least one base (3).

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 *)

Prog

(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, ", ")))

Crossrefs

Cf. A005188.

Cf. A256360, A256361, A256362, A256363, A256364, A256365 (1 to 6 bases).

Cf. A256459 (first occurrences).

Sequence in context: A280537 A022413 A078781 * A287073 A022160 A022158

Adjacent sequences: A256356 A256357 A256358 * A256360 A256361 A256362

Keyword

nonn,base

Author

Tim Johannes Ohrtmann, Mar 26 2015

Status

approved