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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.

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

Original entry on oeis.org

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

Views

Author

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

Keywords

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

A338071 Values of w(k) when w(k-2), w(k-1), and w(k) are all odd, where w is A336957.

Original entry on oeis.org

3263, 7183, 11671, 16291, 16601, 20741, 23257, 28639, 37667, 33163, 38819, 43849, 51469, 52789, 48701, 50275, 63323, 65117, 67903, 67223, 79751, 72193, 71265, 79183, 80743, 74741, 106483, 90571, 94159, 104467, 108043, 135821, 109771, 112561, 119149, 149387, 116377, 137951
Offset: 1

Views

Author

N. J. A. Sloane, Oct 19 2020

Keywords

Comments

See comments in A337644.
It would be nice to understand what is special about these numbers. The majority of them appear to products of two distinct primes. There seems to be very little overlap with either A337646 or A338057, although 1531513 appears both here and in A337646.

Examples

			The factorizations of the first 10 terms are:
1, (13)*(251)
2, (11)*(653)
3, (11)*(1061)
4, (11)*(1481)
5, (13)*(1277)
6, (7)*(2963)
7, (13)*(1789)
8, (13)*(2203)
9, (7)*(5381)
10, (13)*(2551)
The factorizations of terms 555 through 575 are:
555, (11)*(118681)
556, (7)*(213833)
557, (7)*(213887)
558, (11)*(118901)
559, (3)*(5)*(83059)
560, (11)*(120619)
561, (13)*(98867)
562, (11)*(121021)
563, (13)*(99391)
564, (7)*(218873)
565, (11)*(121621)
566, (13)*(99571)
567, (13)*(99989)
568, (11)*(122299)
569, (13)*(122503)
570, (11)*(122533)
571, (11)*(122579)
572, (13)*(100537)
573, (7)*(221537)
574, (11)*(123427)
575, (31)*(38393)

Links

Crossrefs

Cf. A336957, A337644, A337646, A338057, A338070.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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