%I #15 Jan 28 2023 14:00:56

%S 1,5,25,125,625,3125,15625,78125,1953125,9765625,48828125,

%T 762939453125,3814697265625,931322574615478515625,

%U 116415321826934814453125,34694469519536141888238489627838134765625

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

%C Probably finite. Is 34694469519536141888238489627838134765625 the largest term?

%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_607.htm">Puzzle 607. A zeroless Prime power</a>, on primepuzzles.net, Sept. 24, 2011.

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

%F A000351 intersect A052382.

%t Select[5^Range[0,60],DigitCount[#,10,0]==0&] (* _Harvey P. Dale_, Aug 30 2016 *)

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

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

%K nonn,base

%O 1,2

%A _M. F. Hasler_, Sep 25 2011

%E Keyword:fini removed by _Jianing Song_, Jan 28 2023 as finiteness is only conjectured.