A172258 Primes p such that exactly one of the numbers 2p-3 and 2p+3 is prime.

2, 3, 11, 19, 23, 29, 31, 37, 41, 47, 71, 73, 83, 89, 101, 107, 139, 173, 181, 191, 197, 199, 211, 227, 229, 233, 241, 251, 263, 269, 277, 307, 311, 317, 331, 337, 347, 349, 353, 373, 379, 383, 397, 409, 421, 431, 433, 439, 443, 457, 461, 463, 467, 503, 509

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 30 2010

Keywords

• nonn

Examples

			a(1)=2 because 2*2-3=1 (nonprime) and 2*2+3=7 (prime);
a(2)=29 because 2*29-3=55 (nonprime) and 2*29+3=61 (prime).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A092110, A131426.

Programs

Maple

a := proc (n): if isprime(n) = true and isprime(2*n-3) = true and isprime(2*n+3) = false then n elif isprime(n) = true and isprime(2*n-3) = false and isprime(2*n+3) = true then n else end if end proc: seq(a(n), n = 1 .. 700); # Emeric Deutsch, Feb 15 2010

Mathematica

Select[Prime[Range[100]],Total[Boole[PrimeQ[2#+{3,-3}]]]==1&] (* Harvey P. Dale, Mar 27 2021 *)

Extensions

Definition edited by Emeric Deutsch, Feb 15 2010

Corrected and extended by Emeric Deutsch, Feb 15 2010