A305934 - OEIS

%I #42 Jul 02 2018 01:48:39

%S 59049,14348907,43046721,129140163,387420489,3486784401,847288609443,

%T 68630377364883,328256967394537077627,26588814358957503287787,

%U 717897987691852588770249,6461081889226673298932241,1144561273430837494885949696427,22528399544939174411840147874772641,67585198634817523235520443624317923

%N Powers of 3 that have exactly one digit '0' in base 10.

%C Motivated by A030700: decimal expansion of 3^n contains no zeros (probably finite).

%C It appears that this sequence is finite. Is a(15) = 3^73 the last term?

%C There are no more terms through at least 3^(10^7) (which is a 4771213-digit number). It seems nearly certain that no power of 3 containing this many or more decimal digits could have fewer than two '0' digits. (Among numbers of the form 3^k with 73 < k <= 10^7, the only one having fewer than two '0' digits among its final 200 digits is 3^5028978.) - _Jon E. Schoenfield_, Jun 24 2018

%C The first 6 terms coincide with A305931: powers of 3 having at least one digit 0, with complement A238939 (within A000244: powers of 3) conjectured to be finite, too. Then, a(7..8) = A305931(9..10), etc.

%F a(n) = 3^A305933(1,n).

%t Select[3^Range[120], DigitCount[#, 10, 0] == 1 &] (* _Michael De Vlieger_, Jul 01 2018 *)

%o (PARI) for(n=1,99, #select(t->!t,digits(3^n))==1&& print1(3^n","))

%Y Cf. A030700: decimal expansion of 3^n contains no zeros (probably finite), A238939: powers of 3 with no digit '0' in their decimal expansion, A000244: powers of 3.

%Y Subsequence of A305931: powers of 3 having at least one '0'.

%Y Cf. A305933: row n = { k | 3^k has n digits '0' }.

%K nonn,base

%O 1,1

%A _M. F. Hasler_ (following a suggestion by _Zak Seidov_), Jun 14 2018