A179768 Semiprimes of form p*q with p < q, such that 2^p - 1 == 0 (mod q).

6, 21, 155, 253, 889, 979, 1081, 6757, 8251, 13861, 18533, 31987, 32047, 34453, 60581, 64261, 73153, 106483, 110497, 114481, 126253, 212111, 212273, 256507, 258121, 325967, 337133, 351541, 371953, 383183, 392941, 417917, 457207, 482653, 548047, 869221, 933661, 946051

Offset

1,1

Comments

Number of terms < 10^k: 1, 2, 6, 9, 17, 38, 91, 222, ..., .

Links

Robert Israel, Table of n, a(n) for n = 1..518

Example

6 is a term because 6=2*3 and 2^2-1 (mod 3)=0;
21 is a term because 21=3*7 and 2^3-1 (mod 7)=0;
155 is a term because 155=5*31 and 2^5-1 (mod 31)=0;
253 is a term because 253=11*23 and 2^11-1 (mod 23)=0;
889 is a term because 889=7*127 and 2^7-1 (mod 127)=0;
979 is a term because 979=11*89 and 2^11-1 (mod 89)=0; etc.

Maple

N:= 10^6: # to get all terms <= N
Q:= ceil(fsolve(q*log[2](q)=N));
Res:= NULL:
q:= 2:
do
  q:= nextprime(q);
  if q > Q then break fi;
  p:= numtheory:-order(2, q);
  if not isprime(p) then next fi;
  v:= p*q;
  if v <= N then Res:= Res, v  fi
od:
sort([Res]); # Robert Israel, Nov 23 2019

Mathematica

fQ[n_] := Block[{fi = FactorInteger@ n}, Plus @@ Last /@ fi == 2 && PowerMod[2, fi[[1, 1]], fi[[2, 1]]] == 1]; Select[ Range@ 1000000, fQ] (* Robert G. Wilson v, Jan 10 2011 *)

Crossrefs

Cf. A000079, A001358.

Sequence in context: A054366 A304264 A210443 * A131960 A372137 A244299

Adjacent sequences: A179765 A179766 A179767 * A179769 A179770 A179771

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 10 2011

Extensions

Corrected, extended & edited by Robert G. Wilson v, Jan 10 2011

Status

approved