A133123 Double Sophie Germain semiprimes: semiprimes s such that s1=2s+1 and s2=2s1+1 are also semiprimes.

38, 46, 106, 129, 133, 145, 169, 201, 203, 235, 289, 291, 298, 334, 335, 381, 407, 417, 458, 489, 497, 529, 538, 579, 583, 597, 623, 626, 649, 685, 689, 694, 707, 758, 767, 781, 815, 898, 899, 921, 926, 959, 995, 1073, 1079, 1082, 1094, 1099, 1139, 1142

Offset: 1

Author

Zak Seidov, Sep 19 2007

Keywords

• nonn

Comments

Numbers n such that both n and 2n+1 are in A111153.

If 29+30*k, 39+40*k and 47+48*k are all primes then 58+60*k is in the sequence. Thus Dickson's conjecture implies this sequence is infinite. - Robert Israel, Mar 17 2019

Examples

			38=2*19, 2*38+1=77=7*11 and 2*77+1=155=5*31;
129=3*43, 2*129+1=259=7*37 and 2*259+1=519=3*173.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A111153.

Programs

Maple

filter:= n -> andmap(numtheory:-bigomega=2, [n,2*n+1,4*n+3]):
select(filter, [$1..2000]); # Robert Israel, Mar 17 2019

Mathematica

fQ[n_]:=2==Plus@@Last/@FactorInteger[n];Select[Range[2000],fQ[ # ]&&fQ[2#+1]&&fQ[4#+3]&]

Formula

n, n1=2n+1 and n2=2n1+1 are semiprimes.