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A186645 Numbers n such that 2^(n-1) == 1 + b*n (mod n^2), where b divides n-1. 1
3, 7, 11, 13, 19, 29, 31, 37, 71, 127, 379, 491, 2047, 2633, 2659, 3373, 8191, 13249, 26893, 70687, 74597, 87211, 131071, 184511, 524287, 642581, 1897121, 2676301, 2703739, 8388607, 15456151, 52368101, 102785339, 126233057, 193481677, 536870911, 856645921, 1552107133, 2001907169, 2147483647, 2935442621, 3668158729, 6004262437 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All composites in this sequence are 2-pseudoprimes, A001567.

The sequence contains all Mersenne numbers, A001348, n=2^p-1 for primes p (for which b=(n-1)/p). Correspondingly, the composites in this sequence contain all terms of A065341.

The sequence also contains composites of the form 2^A001567(k) - 1, which do not belong to A065341. The existence of composites in the sequence that are not of the form 2^x-1 is unclear.

The sequence contains A125854 as a subsequence.

LINKS

Table of n, a(n) for n=1..43.

MAPLE

isA186645 := proc(n)

        if Power(2, n-1) mod n = 1 then

                x := Power(2, n-1) mod (n^2) ;

                b := (x-1)/n ;

                if b>0 then if modp(n-1, b) = 0 then true; else false; end if;

                else false;

                end if;

        else

                false;

        end if;

end proc:

for n from 1 do if isA186645(n) then printf("%d, \n", n); end if; end do: # R. J. Mathar, Mar 09 2011

CROSSREFS

Sequence in context: A256863 A136087 A091250 * A077256 A067542 A129748

Adjacent sequences:  A186642 A186643 A186644 * A186646 A186647 A186648

KEYWORD

nonn

AUTHOR

Alzhekeyev Ascar M, Feb 25 2011

EXTENSIONS

Edited and more terms added by Max Alekseyev, Mar 14 2011

STATUS

approved

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Last modified January 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)