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A243428 Semiprimes A001358(n) such that A001358(n) + 2^n is also a semiprime. 1
4, 6, 10, 14, 22, 25, 35, 39, 95, 123, 129, 177, 289, 309, 327, 355, 415, 445, 471, 497, 543, 689 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Generated by n = 1, 2, 4, 5, 8, 9, 13, 15, 34, 42, 43, 57, 90, 99, 105, 112, 131, 136, 145, 153, 170, 184, ...

LINKS

Table of n, a(n) for n=1..22.

EXAMPLE

4 is in this sequence because A001358(1) + 2^1 = 6 is also semiprime.

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 *)

PROG

(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

CROSSREFS

Cf. A001358.

Sequence in context: A287375 A137860 A184335 * A091376 A100484 A076924

Adjacent sequences:  A243425 A243426 A243427 * A243429 A243430 A243431

KEYWORD

nonn,less

AUTHOR

Juri-Stepan Gerasimov, Jun 05 2014

EXTENSIONS

One term inserted, and more terms from Colin Barker, Jun 05 2014

STATUS

approved

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Last modified March 18 16:30 EDT 2019. Contains 321292 sequences. (Running on oeis4.)