A174838 Numbers k such that semiprime(k)+1 is prime, where semiprime(k) is A001358.

1, 2, 4, 8, 16, 21, 27, 35, 55, 58, 76, 84, 111, 113, 120, 143, 147, 155, 176, 183, 218, 252, 258, 265, 294, 304, 348, 377, 383, 387, 403, 424, 435, 444, 464, 525, 548, 582, 585, 593, 600, 633, 690, 694, 732, 787, 803, 810, 827, 841, 846, 877, 892, 900, 971

Offset

1,2

Comments

N is in the sequence iff semiprime(n) is of the form 2p where p is a Sophie Germain prime (A005384).

Links

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

Example

a(1)=1 because semiprime(1)+1=5=prime, a(2)=2 because semiprime(2)+1=7=prime, a(3)=4 because semiprime(4)+1=11=prime.

Maple

N:= 1000: # for terms <= N
R:= NULL:
s:= 0:
for x from 1 while s <= N do
  if numtheory:-bigomega(x) = 2 then
    s:= s+1;
    if isprime(x+1) then R:= R, s fi
  fi
od:
R; # Robert Israel, Nov 03 2025

Crossrefs

Cf. A000040, A001358, A005384.

Sequence in context: A350414 A045776 A102252 * A308149 A196871 A334423

Adjacent sequences: A174835 A174836 A174837 * A174839 A174840 A174841

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 30 2010

Extensions

Edited, corrected and extended by Ray Chandler, Apr 05 2010

Status

approved