A305931 Powers of 3 having at least one digit '0' in their decimal representation.

59049, 14348907, 43046721, 129140163, 387420489, 3486784401, 10460353203, 31381059609, 847288609443, 68630377364883, 205891132094649, 1853020188851841, 5559060566555523, 50031545098999707, 150094635296999121, 450283905890997363, 1350851717672992089, 4052555153018976267, 12157665459056928801

Offset: 1

Author

M. F. Hasler, Jun 15 2018

Keywords

• nonn
• base
• easy

Comments

The analog of A298607 for 3^k instead of 2^k.

The complement A238939 is conjectured to have only 23 elements, the largest being 3^68. Thus, all larger powers of 3 are (conjectured to be) in this sequence. Each of the subsequences "powers of 3 with exactly n digits 0" is conjectured to be finite. Provided there is at least one such element for each n >= 0, this leads to a partition of the integers, given in A305933.

Crossrefs

Cf. A030700 = row 0 of A305933: decimal expansion of 3^n contains no zeros.

Complement (within A000244: powers of 3) of A238939: powers of 3 with no digit '0' in their decimal expansion.

Analog of A298607: powers of 2 with the digit '0' in their decimal expansion.

The first six terms coincide with the finite sequence A305934: powers of 3 having exactly one digit 0.

Programs

Mathematica

Select[3^Range[0,40],DigitCount[#,10,0]>0&] (* Harvey P. Dale, May 30 2020 *)

PARI

for(k=0,69, vecmin(digits(3^k))|| print1(3^k","))

PARI

select( t->!vecmin(digits(t)), apply( k->3^k, [0..40]))