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A133123 Double Sophie Germain semiprimes: semiprimes s such that s1=2s+1 and s2=2s1+1 are also semiprimes. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 20:20 EDT 2021. Contains 345425 sequences. (Running on oeis4.)