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 A007844 #27 Dec 30 2019 12:22:02 %S A007844 1,3,6,9,9,12,15,18,18,21,24,27,27,27,30,33,36,36,39,42,45,45,48,51, %T A007844 54,54,54,57,60,63,63,66,69,72,72,75,78,81,81,81,81,84,87,90,90,93,96, %U A007844 99,99,102,105,108,108,108,111,114,117,117,120,123,126,126,129,132,135,135,135 %N A007844 Least positive integer k for which 3^n divides k!. %C A007844 It appears than for n>0, a(n) is divisible by 3, and that the resulting sequence a(n)/3 is A120503 (checked up to n=1000). - _Michel Marcus_, Aug 19 2013. [This is true: see A007843 for the idea of the proof. - _M. F. Hasler_, Dec 27 2019] %C A007844 Also least positive integer k for which 6^n divides k!. - _Michel Marcus_, Aug 20 2013 %D A007844 H. Ibstedt, Smarandache Primitive Numbers, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 216-229. %H A007844 T. D. Noe, <a href="/A007844/b007844.txt">Table of n, a(n) for n = 0..1000</a> %H A007844 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a> %F A007844 a(n) = 3*A120503(n) for n > 0, cf. A007843. - _M. F. Hasler_, Dec 27 2019 %t A007844 Array[Block[{k = 1}, While[Mod[k!, 3^#] != 0, k++]; k] &, 67, 0] (* _Michael De Vlieger_, Dec 29 2019 *) %o A007844 (PARI) a(n) = {k = 1; while (valuation(k!, 3) < n, k++); k;} \\ _Michel Marcus_, Aug 19 2013 %o A007844 (PARI) apply( A007844(n)={my(s=sumdigits(n*=2,3)\2); n-=n%3; while(s>0, s-=valuation(n+=3,3)); n+!n}, [0..99]) \\ _M. F. Hasler_, Dec 27 2019 %Y A007844 Cf. A007843 (analog for 2), A007845 (analog for 5). %Y A007844 Cf. A120503 (Meta-Fibonacci, k = 3). %K A007844 nonn %O A007844 0,2 %A A007844 Bruce Dearden and _Jerry Metzger_, R. Muller