A186884 Numbers k such that 2^(k-1) == 1 + b*k (mod k^2), where b divides k - 2^p for some integer p >= 0 and 2^p <= b.

3, 5, 7, 11, 13, 17, 19, 29, 31, 37, 71, 127, 173, 199, 233, 251, 257, 379, 491, 613, 881, 2047, 2633, 2659, 3373, 3457, 5501, 5683, 8191, 11497, 13249, 15823, 16879, 18839, 22669, 24763, 25037, 26893, 30139, 45337, 48473, 56671, 58921, 65537, 70687, 74531, 74597, 77023, 79669, 87211, 92237, 102407, 131071, 133493, 181421, 184511, 237379, 250583, 254491, 281381

Offset

1,1

Comments

This sequence contains A186645 as a subsequence (corresponding to p=0).

All composites in this sequence are 2-pseudoprimes, A001567. This sequence contains all terms of A054723. Another composite term is 4294967297 = 2^32 + 1, which does not belong to A054723. In other words, all known composite terms have the form (2^x + 1) or (2^x - 1). Are there composites not of this form?

This sequence contains all the primes of the forms (2^x + 1) and (2^x - 1), i.e., subsequences A092506 and A000668.

Links

Table of n, a(n) for n=1..60.

Crossrefs

Sequence in context: A065041 A065393 A179740 * A045393 A132143 A239879

Adjacent sequences: A186881 A186882 A186883 * A186885 A186886 A186887

Keyword

nonn

Author

Alzhekeyev Ascar M, Feb 28 2011

Extensions

Edited by Max Alekseyev, Mar 14 2011

a(25) and a(26) interchanged by Georg Fischer, Jul 08 2022

Status

approved