This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A305931 #7 May 30 2020 17:35:12 %S A305931 59049,14348907,43046721,129140163,387420489,3486784401,10460353203, %T A305931 31381059609,847288609443,68630377364883,205891132094649, %U A305931 1853020188851841,5559060566555523,50031545098999707,150094635296999121,450283905890997363,1350851717672992089,4052555153018976267,12157665459056928801 %N A305931 Powers of 3 having at least one digit '0' in their decimal representation. %C A305931 The analog of A298607 for 3^k instead of 2^k. %C A305931 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. %t A305931 Select[3^Range[0,40],DigitCount[#,10,0]>0&] (* _Harvey P. Dale_, May 30 2020 *) %o A305931 (PARI) for(k=0,69, vecmin(digits(3^k))|| print1(3^k",")) %o A305931 (PARI) select( t->!vecmin(digits(t)), apply( k->3^k, [0..40])) %Y A305931 Cf. A030700 = row 0 of A305933: decimal expansion of 3^n contains no zeros. %Y A305931 Complement (within A000244: powers of 3) of A238939: powers of 3 with no digit '0' in their decimal expansion. %Y A305931 Analog of A298607: powers of 2 with the digit '0' in their decimal expansion. %Y A305931 The first six terms coincide with the finite sequence A305934: powers of 3 having exactly one digit 0. %K A305931 nonn,base,easy %O A305931 1,1 %A A305931 _M. F. Hasler_, Jun 15 2018