A256362 Numbers that are multiple-digit narcissistic numbers in exactly three bases.

125, 325, 370, 793, 845, 1125, 1445, 2080, 2125, 2925, 3125, 3200, 3725, 3757, 5050, 5265, 6125, 6250, 6845, 7605, 8125, 8405, 10125, 10261, 10440, 10625, 11250, 13005, 13690, 14365, 15125, 15925, 18785, 22100

Offset

1,1

Links

Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..445

W. Schneider, Perfect Digital Invariants: Pluperfect Digital Invariants(PPDIs)

Eric Weisstein's World of Mathematics, Narcissistic Number

Wikipedia, Narcissistic number

Example

a(1) = 125 because this is the first number that is a multiple-digit narcissistic number in exactly three bases (12, 23 and 57).

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==3, print1(n, ", ")))

Crossrefs

Cf. A005188.

Cf. A256359 (every number of bases).

Cf. A256360, A256361, A256363, A256364, A256365 (1, 2, 4, 5 and 6 bases).

Cf. A256459 (first occurrences).

Sequence in context: A338469 A253226 A223182 * A175486 A250579 A161855

Adjacent sequences: A256359 A256360 A256361 * A256363 A256364 A256365

Keyword

nonn,base

Author

Tim Johannes Ohrtmann, Mar 26 2015

Status

approved