A195942 Zeroless prime powers (excluding primes): Intersection of A025475 and A052382.

1, 4, 8, 9, 16, 25, 27, 32, 49, 64, 81, 121, 125, 128, 169, 243, 256, 289, 343, 361, 512, 529, 625, 729, 841, 961, 1331, 1369, 1681, 1849, 2187, 2197, 3125, 3481, 3721, 4489, 4913, 5329, 6241, 6561, 6859, 6889, 7921, 8192

Offset: 1

Author

M. F. Hasler, Sep 25 2011

Keywords

• nonn
• base
• easy

Links

• Reinhard Zumkeller and T. D. Noe, Table of n, a(n) for n = 1..4094 (terms < 10^10)
• C. Rivera, Puzzle 607. A zeroless Prime power, on primepuzzles.net, Sept. 24, 2011.

Crossrefs

Cf. A195985, A195943, A195944, A195945, A195946, A195908, A195948, A007377, A008839, A030700, A030701, A030702, A030703, A030704, A030705, A030706.

Programs

Haskell

a195942 n = a195942_list !! (n-1)
a195942_list = filter (\x -> a010051 x == 0 && a010055 x == 1) a052382_list
-- Reinhard Zumkeller, Sep 27 2011

Mathematica

mx = 10^10; t = {1}; p = 2; While[pw = 2; While[n = p^pw; n <= mx, If[Union[IntegerDigits[n]][[1]] > 0, AppendTo[t, n]]; pw++]; pw > 2, p = NextPrime[p]]; t = Sort[t] (* T. D. Noe, Sep 27 2011 *)

PARI

for( n=1,9999, is_A025475(n) && is_A052382(n) && print1(n","))

Formula

A195942 = A025475 intersect A052382.

A010055(a(n)) * (1 - A010051(a(n))) * A168046(a(n)) = 1. - Reinhard Zumkeller, Sep 27 2011