A195948 Powers of 5 which have no zero in their decimal expansion.

1, 5, 25, 125, 625, 3125, 15625, 78125, 1953125, 9765625, 48828125, 762939453125, 3814697265625, 931322574615478515625, 116415321826934814453125, 34694469519536141888238489627838134765625

Offset: 1

Author

M. F. Hasler, Sep 25 2011

Keywords

• nonn
• base

Comments

Probably finite. Is 34694469519536141888238489627838134765625 the largest term?

Links

• C. Rivera, Puzzle 607. A zeroless Prime power, on primepuzzles.net, Sept. 24, 2011.

Crossrefs

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

Programs

Mathematica

Select[5^Range[0,60],DigitCount[#,10,0]==0&] (* Harvey P. Dale, Aug 30 2016 *)

PARI

for( n=0,9999, is_A052382(5^n) && print1(5^n,","))

Formula

a(n) = 5^A008839(n).

A000351 intersect A052382.

Extensions

Keyword:fini removed by Jianing Song, Jan 28 2023 as finiteness is only conjectured.