A353004 Numbers k such that 2*k^2 + 29 is semiprime.

29, 30, 32, 35, 39, 44, 50, 57, 58, 61, 63, 65, 72, 74, 76, 84, 87, 88, 89, 91, 92, 94, 95, 97, 99, 102, 107, 109, 113, 116, 118, 120, 122, 123, 125, 126, 127, 134, 138, 144, 145, 146, 147, 148, 149, 150, 153, 154, 156, 157, 163, 164, 165, 166, 169, 174, 175, 179, 180, 182, 183, 191, 194, 196, 200

Offset

1,1

Comments

The least positive k for which 2*k^2 + 29 is neither prime nor semiprime is k = 185, which gives 2*k^2 + 29 = 68479 = 31*47^2.

Links

Table of n, a(n) for n=1..65.

Example

a(5) = 39; 2*39^2 + 29 = 3071 = 37*83 is semiprime.

Mathematica

Select[Range[200], PrimeOmega[2*#^2 + 29] == 2 &] (* Amiram Eldar, Apr 15 2022 *)

Prog

(Python)
from sympy import primeomega
def semiprime(n): return primeomega(n) == 2
print([k for k in range(140) if semiprime(2*k**2+29)]) # Michael S. Branicky, Apr 15 2022
(PARI) isok(k) = bigomega(2*k^2+29) == 2; \\ Michel Marcus, Apr 15 2022

Crossrefs

Subsequence of A007642, whose first term not in this sequence is 185.

Cf. A241554, A352949, A353388.

Sequence in context: A165850 A129287 A007642 * A295749 A022399 A042694

Adjacent sequences: A353001 A353002 A353003 * A353005 A353006 A353007

Keyword

nonn

Author

Rémi Guillaume, Apr 15 2022

Status

approved