A172072 Numbers k such that either prime(k) - 5/2 +- 7/2 is prime.

1, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 19, 21, 22, 24, 27, 28, 29, 30, 33, 37, 38, 40, 41, 45, 46, 50, 51, 52, 55, 56, 57, 59, 61, 65, 66, 68, 71, 72, 74, 75, 77, 85, 87, 90, 91, 97, 101, 103, 104, 106, 108, 109, 111, 112, 114, 118, 119, 120, 124, 130, 131, 134, 144

Offset

1,2

Comments

Also: 1 plus numbers k such that prime(k) - 6 is prime. - Michael S. Branicky, Aug 16 2025

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(1) = 1 because prime(1)-5/2-7/2 = 2-5/2-7/2 = -4 (nonprime) and prime(1)-5/2+7/2 = 2-5/2+7/2 = 3 (prime).

Mathematica

Join[{1}, Select[Range[5, 150], PrimeQ[Prime[#] - 6] &]] (*  Paolo Xausa, Aug 17 2025 *)

Prog

(PARI) is(n, p=prime(n))=isprime(p-6) || isprime(p+1) \\ Charles R Greathouse IV, Jun 13 2017
(Python)
from sympy import isprime, prime
def ok(n): return n == 1 or isprime(prime(n)-6)
print([k for k in range(1, 145) if ok(k)]) # Michael S. Branicky, Aug 16 2025

Crossrefs

Cf. A000040, A046117, A172071.

Sequence in context: A396135 A396127 A120190 * A121542 A182306 A023379

Adjacent sequences: A172069 A172070 A172071 * A172073 A172074 A172075

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 25 2010

Extensions

Corrected (57 inserted) by R. J. Mathar, May 02 2010

Status

approved