A368615 Semiprimes k such that prime(k) - k and prime(k) + k are also semiprimes.

58, 74, 166, 226, 262, 326, 334, 478, 566, 694, 734, 802, 838, 886, 1114, 1142, 1294, 1382, 1514, 1574, 1894, 2038, 2078, 2138, 2858, 3254, 3274, 3314, 3578, 4286, 4306, 4426, 5102, 5242, 5386, 5398, 5578, 5806, 5906, 6022, 6046, 6362, 6866, 7094, 7142, 7246, 7274, 7438, 7694, 7838, 7886, 7934

Offset

1,1

Comments

All terms are even.

Links

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

Formula

Numbers k such that A001222(k) = A001222(A000040(k) - k) = A001222(A000040(k) + k) = 2.

a(n) == 2 (mod 4). - Hugo Pfoertner, Jan 05 2024

Example

a(3) = 166 is a term because the 166th prime is 983, and 166 = 2 * 83, 983 - 166 = 817 = 19 * 43, and 983 + 166 =  1149 = 3 * 383 are all semiprimes.

Maple

p:= 1: R:= NULL: count:= 0:
for k from 2 by 2 while count < 100 do
  p:= nextprime(nextprime(p));
  if isprime(k/2) and numtheory:-bigomega(k+p) = 2 and numtheory:-bigomega(p-k) = 2 then count:= count+1; R:= R, k fi
od:
R;

Mathematica

s = {}; Do[If[{2, 2, 2} == PrimeOmega[{k, Prime[k] + k, Prime[k] - k}], AppendTo[s, k]], {k, 4, 10000}]; s

Crossrefs

Cf. A000040, A001222, A001358.

Sequence in context: A226036 A127024 A010338 * A184074 A281824 A127334

Adjacent sequences: A368612 A368613 A368614 * A368616 A368617 A368618

Keyword

nonn

Author

Zak Seidov and Robert Israel, Dec 31 2023

Status

approved