A352949 -id:A352949 - cp's OEIS frontend

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

Rémi Guillaume, Apr 15 2022

nonn

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.

Includes 29*k if 58*k^2 + 1 is prime; Bunyakovsky's conjecture implies there are infinitely many of these. - Robert Israel, Jul 29 2025

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

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

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

Cf. A241554, A352949, A353388.

filter:= proc(k) numtheory:-bigomega(2*k^2+29) = 2 end proc;
select(filter, [$1..1000]); # Robert Israel, Jul 29 2025

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

isok(k) = bigomega(2*k^2+29) == 2; \\ Michel Marcus, Apr 15 2022

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

cp's OEIS Frontend

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

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