A188063 Numbers n with property that n==5 (mod 12) and 2^(m-1)=1 (mod m) where m=(2*n-1)*n.

17, 281, 677, 953, 2729, 4241, 4637, 18749, 55217, 112997, 115769, 148781, 151733, 326693, 623393, 637841, 744833, 907733, 1056833, 1444481, 1774937, 1831481, 1866737, 1939097, 2028197, 2564369, 2566601, 3146237, 4635317, 4777433, 5629157, 5960501, 6247601, 6837221, 7248737, 7278041, 7340537, 7442849, 7766237

Offset

1,1

Comments

All terms <= 10^9 are prime, are there any composite terms?

Links

Table of n, a(n) for n=1..39.

Mathematica

Select[Range[5, 777*10^4, 12], PowerMod[2, #(2#-1)-1, #(2#-1)]==1&] (* Harvey P. Dale, Sep 07 2021 *)

Prog

(PARI)
{ forstep (n=5, 10^9, 12,
m = (2*n-1)*n;
t = Mod(2, m)^(m-1);
if ( component(t, 2) == 1,
   print1(n, ", "); /* print term */
  /* if ( !isprime(n), print1(n, ", ") ); */ /* print only nonprime terms */
); ); } /* Joerg Arndt, Apr 01 2011 */

Crossrefs

Sequence in context: A113076 A159503 A245940 * A012235 A196743 A196901

Adjacent sequences: A188060 A188061 A188062 * A188064 A188065 A188066

Keyword

nonn

Author

Alzhekeyev Ascar M, Mar 20 2011

Status

approved