

A190213


Let k=2^n1 and m=1+(k1)*(n1), x=m*k and define remainders a and b via 2^(x1) == (a+1) (mod x) and m^(x1) == (b+1) (mod x). If a == 0 (mod k) and b == 0 (mod k), n is in the sequence.


0



1, 3, 4, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Conjecture: All odd entries are also Mersenne exponents (A000043): primes n such that 2^n1 is prime.


LINKS

Table of n, a(n) for n=1..19.


EXAMPLE

For n=3, k=2^31=7, m=1+6*2=13, x=m*k=13*7=91, 2^(x1)==(a+1) (mod x) with 2^90 == (63+1)(mod 91), fixes a=63. m^(x1) == (b+1) (mod x) with 13^90 == (77+1) (mod 91) fixes b=77. The two conditions are satisfied: 63 == 0 (mod 7) and 77 == 0 (mod 7). Therefore n=3 is in the sequence.


MAPLE

isA190213 := proc(n) local k, m, x, a, b ; k := 2^n1 ; m := (k1)*(n1)+1 ; x := k*m ; a := modp( 2 &^ (x1), x) 1 ; b := modp( m &^ (x1), x) 1 ; return ( modp(a, k) = 0 and modp(b, k)=0 ) ; end proc:
for n from 2 do if isA190213(n) then printf("%d, \n", n); end if; end do; # avoids n=1 and undefined 0^0, R. J. Mathar, Jun 11 2011


CROSSREFS

Cf. A144671, A000043.
Sequence in context: A139440 A102607 A079463 * A216574 A216561 A192269
Adjacent sequences: A190210 A190211 A190212 * A190214 A190215 A190216


KEYWORD

nonn,more


AUTHOR

Alzhekeyev Ascar M, May 19 2011


STATUS

approved



