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 A172287 Primes p such that exactly one of 2p-3 and 3p-2 is prime. 5

%I

%S 17,31,41,47,61,83,97,101,103,107,157,163,223,233,241,257,271,277,283,

%T 293,307,311,313,317,337,401,421,457,467,491,521,523,541,547,557,563,

%U 577,593,601,613,617,631,641,643,647,653,661,673,677,701,743,761,773

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

%C 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

%C No terms end in 9. Dickson's conjecture implies that there are infinitely many terms. - _Robert Israel_, Jul 02 2015

%H Reinhard Zumkeller, <a href="/A172287/b172287.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1)=17 because 2*17-3=31 is prime and 3*17-2=49 is nonprime.

%e 19 is not a term because neither 2*19-3=35 nor 3*19-2=55 is prime;

%e 23 is not a term because both 2*23-3=43 and 3*23-2=67 are prime.

%p 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

%t Select[Prime@ Range@ 150, Xor[PrimeQ[2 # - 3], PrimeQ[3 # - 2]] &] (* _Michael De Vlieger_, Jul 01 2015 *)

%o a172287 n = a172287_list !! (n-1)

%o a172287_list = filter

%o (\p -> a010051' (2 * p - 3) + a010051' (3 * p - 2) == 1) a000040_list

%o -- _Reinhard Zumkeller_, Jul 02 2015

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

%K nonn,easy

%O 1,1

%A _Juri-Stepan Gerasimov_, Jan 30 2010

%E Extended by _Charles R Greathouse IV_, Mar 25 2010

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Last modified July 14 15:44 EDT 2020. Contains 335729 sequences. (Running on oeis4.)