cp's OEIS Frontend

A337644 Numbers k such that w(k), w(k+1), and w(k+2) are all odd, where w is A336957.

%I A337644 #50 Nov 05 2023 09:04:21
%S A337644 2128,4689,7742,11011,11508,12277,16398,20227,22556,23709,26922,31455,
%T A337644 36016,36857,39014,39563,45804,47213,47738,48847,48932,50805,53062,
%U A337644 57575,58784,60281,63594,66251,68872,74021,79238,84175,89428,91709,92902,92947,94404,98317
%N A337644 Numbers k such that w(k), w(k+1), and w(k+2) are all odd, where w is A336957.
%C A337644 These terms are rare, since most of the time the parity of A336957 follows the pattern 1, 0,0, 1,1, 0,0, 1,1, 0,0, ... It would be useful to have a proof that the present sequence is (or is not) infinite. The graph strongly suggests it is an infinite sequence.
%C A337644 It is also possible that eventually there will be four or more odd terms in succession. However, this does not happen in the first eleven million terms, so probably it never happens.
%C A337644 If w(j) is even and w(j+1) is odd, then w(j+2) is forced to be also odd. In most cases w(j+3) is then even, but is occasionally odd (giving three odds in a row), and then the values of j+1 are given in the present sequence. For understanding the growth of A336957, the values of j+3 and w(j+3) are also important, and are given in A338070 and A338071, respectively.
%H A337644 N. J. A. Sloane, <a href="/A337644/b337644.txt">Table of n, a(n) for n = 1..5985</a> (computed from Frank Stevenson's file of the first 11333576 terms of A336957; terms 1..71 from N. J. A. Sloane, terms 72..575 from Scott R. Shannon)
%Y A337644 Cf. A336957, A338070, A338071.
%K A337644 nonn
%O A337644 1,1
%A A337644 _Scott R. Shannon_ and _N. J. A. Sloane_, Sep 24 2020
%E A337644 Comments revised by _N. J. A. Sloane_, Oct 12 2020