A172287 Primes p such that exactly one of 2p-3 and 3p-2 is prime.

17, 31, 41, 47, 61, 83, 97, 101, 103, 107, 157, 163, 223, 233, 241, 257, 271, 277, 283, 293, 307, 311, 313, 317, 337, 401, 421, 457, 467, 491, 521, 523, 541, 547, 557, 563, 577, 593, 601, 613, 617, 631, 641, 643, 647, 653, 661, 673, 677, 701, 743, 761, 773

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 30 2010

Keywords

• nonn
• easy

Comments

A010051(2*a(n)+3) + A010051(3*a(n)+2) = 1; each term is either a term of A063908 or of A088878. - Reinhard Zumkeller, Jul 02 2015

No terms end in 9. Dickson's conjecture implies that there are infinitely many terms. - Robert Israel, Jul 02 2015

Examples

			a(1)=17 because 2*17-3=31 is prime and 3*17-2=49 is nonprime.
19 is not a term because neither 2*19-3=35 nor 3*19-2=55 is prime;
23 is not a term because both 2*23-3=43 and 3*23-2=67 are prime.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A010051, A063908, A088878, A259730.

Programs

Haskell

a172287 n = a172287_list !! (n-1)
a172287_list = filter
   (\p -> a010051' (2 * p - 3) + a010051' (3 * p - 2) == 1) a000040_list
-- Reinhard Zumkeller, Jul 02 2015

Maple

A172287:=n->`if`(isprime(n) and (isprime(2*n-3) xor isprime(3*n-2)), n, NULL): seq(A172287(n), n=1..1000); # Wesley Ivan Hurt, Jun 23 2015

Mathematica

Select[Prime@ Range@ 150, Xor[PrimeQ[2 # - 3], PrimeQ[3 # - 2]] &] (* Michael De Vlieger, Jul 01 2015 *)

Extensions

Extended by Charles R Greathouse IV, Mar 25 2010