A067604 Smallest prime p of two consecutive primes, p < q, such that gcd(p+1, q+1) = 2n.

3, 7, 23, 359, 139, 467, 293, 3391, 1259, 17519, 3739, 7079, 12011, 52639, 18869, 66239, 77383, 27143, 51071, 76039, 119447, 76163, 91033, 226943, 206699, 894451, 327347, 492911, 399793, 195599, 313409, 981823, 829883, 1169939, 302329

Offset: 1

Author

Robert G. Wilson v, Jan 31 2002

Keywords

• nonn

Comments

Since all consecutive primes, p < q and p greater than 2, are odd, therefore gcd(p+1, q+1) must be even.

Examples

			a(1) = 3, the 3rd prime being the first entry in A066940;
a(2) = 7, the 4th prime being the first entry in A066941;
a(3) = 23, the 9th prime being of the first entry in A066942;
a(4) = 359, the 72nd prime being the first entry in A066943;
a(5) = 139, the 34th prime being the first entry in A066944.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A066940, A066941, A066942, A066944, A067603.

Programs

Mathematica

a = Table[0, {100}]; p = 3; q = 5; Do[q = Prime[n + 1]; d = GCD[p + 1, q + 1]/2; If[d < 101 && a[[d]] == 0, a[[d]] = n]; b = c, {n, 2, 10^7}]; Prime[a]

PARI

a(n)=my(k=2*n); forstep(p=k-1,oo,k, if(isprime(p) && (nextprime(p+1)-p)%k==0, return(p))) \\ Charles R Greathouse IV, Aug 17 2015