A072666 Numbers n such that prime(n) + prime(n+1) - 1 is prime.

2, 3, 4, 5, 6, 8, 10, 11, 13, 14, 18, 19, 21, 25, 30, 31, 36, 41, 43, 44, 46, 47, 48, 50, 52, 53, 58, 59, 60, 62, 63, 66, 68, 70, 73, 74, 75, 78, 79, 80, 81, 83, 85, 90, 93, 99, 100, 101, 106, 112, 114, 116, 117, 120, 124, 126, 127, 129, 130, 131, 132, 137, 138, 140, 145, 147, 149

Offset: 1

Author

Herman H. Rosenfeld (herm3(AT)pacbell.net), Aug 12 2002

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000720, A072667, A072669, A177017.

Programs

Magma

[n: n in [1..200] | IsPrime(NthPrime(n) + NthPrime(n+1)-1)] // Vincenzo Librandi, Aug 26 2012

Maple

N:= 10^4: # to get all terms n such that prime(n+1) <= N
Primes:= select(isprime,[2,seq(2*i+1,i=1..floor(N/2))]):
PP:= Primes[1..-2]+Primes[2..-1]:
select(t -> isprime(PP[t]-1), [$1..nops(PP)]); # Robert Israel, Dec 11 2014

Mathematica

Select[Range[200], PrimeQ[Prime[#]+Prime[#+1]-1] &] (* Harvey P. Dale, Dec 16 2010 *)

Formula

a(n) = pi(A072667(n)) = A000720(A072667(n)). - Zak Seidov, Dec 08 2014

Extensions

Definition clarified by Robert Israel, Dec 11 2014