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A186884 Numbers n such that 2^(n-1) = 1 + b*n (mod n^2), where b divides n-2^p for some integer p>=0 and 2^p<=b. 0
3, 5, 7, 11, 13, 17, 19, 29, 31, 37, 71, 127, 173, 199, 233, 251, 257, 379, 491, 613, 881, 2047, 2633, 2659, 3457, 3373, 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 (list; graph; refs; listen; history; text; internal format)
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 elements of the sequence A054723. Another composite term is 4294967297 = 2 ^ 32 + 1, which does not belong to A054723. In other words, all known composite numbers 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 form (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

STATUS

approved

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Last modified October 22 09:56 EDT 2019. Contains 328315 sequences. (Running on oeis4.)