A283527 First of three consecutive Sophie Germain semiprimes: n, n+1 and n+2 are all terms of A111153.

15117, 17245, 34413, 93453, 143101, 157713, 190621, 208293, 233097, 294301, 323281, 346497, 470341, 501477, 1306113, 1337221, 1346401, 1655853, 1682313, 1774801, 1877613, 1879021, 1933233, 1976041

Offset: 1

Author

Zak Seidov, Mar 09 2017

Keywords

• nonn

Comments

All terms are 1 mod 4, see A056809.

Links

• Zak Seidov, Table of n, a(n) for n = 1..408

Crossrefs

Subsequence of A056809 and of A111153. Cf. A001358.

Programs

Mathematica

  po[x_] := PrimeOmega[x];   Select[Range[15117, 200000, 2],
2 == po[#] == po[2*# + 1] ==po[# + 1] == po[2*# + 3] == po[# + 2] ==
po[2*# + 5] &]

PARI

{bo(x)=bigomega(x)
forstep(n=15117,2000000,2, if(
2 == bo(n) && 2 == bo(n+1) && 2 == bo(n+2) && 2 == bo(2*n+1) &&
2 == bo(2*n+3) && 2 == bo(2*n+5), print1(n",")))}

PARI

list(lim)=lim\=1; my(v=List(),x=2*lim+5,u=vectorsmall(x)); forprime(p=2,x\2, forprime(q=2,min(lim\p,p), u[p*q]=1)); forstep(n=15117,lim,4, if(u[n] && u[n+1] && u[n+2] && u[2*n+1] && u[2*n+3] && u[2*n+5], listput(v,n))); Vec(v) \\ Charles R Greathouse IV, Mar 10 2017