

A186645


Numbers n such that 2^(n1) == 1 + b*n (mod n^2), where b divides n1.


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 2pseudoprimes, A001567.
The sequence contains all Mersenne numbers, A001348, n=2^p1 for primes p (for which b=(n1)/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^x1 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, n1) mod n = 1 then
x := Power(2, n1) mod (n^2) ;
b := (x1)/n ;
if b>0 then if modp(n1, 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



