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

1,1

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

Links

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

Formula

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

Example

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.

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]&]

Crossrefs

Cf. A111153.

Sequence in context: A031409 A078550 A295491 * A177222 A078539 A282813

Adjacent sequences: A133120 A133121 A133122 * A133124 A133125 A133126

Keyword

nonn

Author

Zak Seidov, Sep 19 2007

Status

approved