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

2128, 4689, 7742, 11011, 11508, 12277, 16398, 20227, 22556, 23709, 26922, 31455, 36016, 36857, 39014, 39563, 45804, 47213, 47738, 48847, 48932, 50805, 53062, 57575, 58784, 60281, 63594, 66251, 68872, 74021, 79238, 84175, 89428, 91709, 92902, 92947, 94404, 98317

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Sep 24 2020

Keywords

• nonn

Comments

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.

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.

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.

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..5985 (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)

Crossrefs

Cf. A336957, A338070, A338071.

Extensions

Comments revised by N. J. A. Sloane, Oct 12 2020