A243428 Semiprimes A001358(n) such that A001358(n) + 2^n is also a semiprime.
4, 6, 10, 14, 22, 25, 35, 39, 95, 123, 129, 177, 289, 309, 327, 355, 415, 445, 471, 497, 543, 689
Offset: 1
Examples
4 is in this sequence because A001358(1) + 2^1 = 6 is also semiprime.
Crossrefs
Cf. A001358.
Programs
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Mathematica
NextSemiPrime[n_, k_: 1] := Block[{c = 0, sgn = Sign[k]}, sp = n + sgn; While[c < Abs[k], While[ PrimeOmega[sp] != 2, If[sgn < 0, sp--, sp++]]; If[ sgn < 0, sp--, sp++]; c++]; sp + If[sgn < 0, 1, -1]]; SemiPrimePi[n_] := Sum[ PrimePi[ n/Prime[i]] - i + 1, {i, PrimePi[ Sqrt[ n]] }]; sp = 4; lst = {}; While[ sp < 1001, If[ PrimeOmega[sp + 2^SemiPrimePi@ sp] == 2, AppendTo[lst, sp]; Print@ sp]; sp = NextSemiPrime@ sp; c++]; lst (* Robert G. Wilson v, Jun 20 2014 *) -
PARI
list(lim)=my(v=List(), t); forprime(p=2, sqrt(lim), t=p; forprime(q=p, lim\t, listput(v, t*q))); vecsort(Vec(v)) \\ From A001358 sp=list(700); s=[]; for(n=1, #sp, if(bigomega(sp[n]+2^n)==2, s=concat(s, sp[n]))); s \\ Colin Barker, Jun 05 2014
Extensions
One term inserted, and more terms from Colin Barker, Jun 05 2014
Comments