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

1,1

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.

Links

Table of n, a(n) for n=1..19.

Mathematica

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

Prog

(PARI) for(k=0, 69, vecmin(digits(3^k))|| print1(3^k", "))
(PARI) select( t->!vecmin(digits(t)), apply( k->3^k, [0..40]))

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.

Sequence in context: A017633 A203653 A016762 * A305934 A016774 A016846

Adjacent sequences: A305928 A305929 A305930 * A305932 A305933 A305934

Keyword

nonn,base,easy

Author

M. F. Hasler, Jun 15 2018

Status

approved