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

Author

Alzhekeyev Ascar M, Feb 28 2011

Keywords

• nonn

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.

Extensions

Edited by Max Alekseyev, Mar 14 2011

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