cp's OEIS Frontend

A292114 List of numbers n such that A039655(n) reaches a new record high.

%I A292114 #35 Nov 07 2017 03:20:44
%S A292114 2,4,9,121,301,441,468,3171,8373,13440,16641,16804,83161,100652,
%T A292114 133200,367428,395640,459680,701823,3739690,4238314,6698616,9014248,
%U A292114 12301860,16956850,22230514,54889200,60676144,84983056,116648892,128942664
%N A292114 List of numbers n such that A039655(n) reaches a new record high.
%C A292114 Naively, one might have expected these numbers to have some other distinguishing property (primorials, perhaps), but that seems not to be the case.
%C A292114 Increasingly many of the values are of the form m*p with a (large) prime p and a smooth m, often m = 2^k (for a(n), n = 12, 14, 21, 23, 26, 28, 29, ...) or m = 2^k*3^k' (n = 7, 9, 19, 22, 30, ...) or m = 2^k*5^k' (n = 20, 25, ...). I conjecture that almost all terms are even. Also, for most terms (n = 1, 2, 3, 4, 5, 7, 10, 12, 14, 15, 16, 17, 19, 20, 21, 23, 24, 25, 26, 29, 30, 31, ...), either a(n)-1 or a(n)+1 has at most 2 prime divisors. - _M. F. Hasler_, Sep 25 2017
%H A292114 Hugo Pfoertner, <a href="/A292114/b292114.txt">Table of n, a(n) for n = 1..48</a>
%H A292114 N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, <a href="https://vimeo.com/237029685">Part I</a>, <a href="https://vimeo.com/237030304">Part 2</a>, <a href="https://oeis.org/A290447/a290447_slides.pdf">Slides.</a> (Mentions this sequence)
%o A292114 (PARI) m=-n=1;until(print1(n","),until(A039655(n++)>m,);m=A039655(n)) \\ _M. F. Hasler_, Sep 25 2017
%Y A292114 Cf. A039654, A039655, A292115.
%K A292114 nonn
%O A292114 1,1
%A A292114 _N. J. A. Sloane_, Sep 22 2017
%E A292114 More terms from _Hugo Pfoertner_, Sep 22 2017