A231506 Primes p such that p + 3*k and p - 3*k, both are primes, where p is k-th prime.

7, 13, 19, 53, 71, 101, 107, 139, 173, 199, 223, 229, 281, 293, 397, 463, 557, 569, 673, 787, 809, 839, 953, 1013, 1283, 1451, 1559, 1657, 1861, 1871, 1877, 1949, 1987, 1997, 2213, 2311, 2347, 2357, 2377, 2503, 2543, 2551, 2593, 2633, 2837, 2851, 2939, 2999, 3041

Offset: 1

Author

K. D. Bajpai, Nov 09 2013

Keywords

• nonn

Examples

			a(7)= 107 which is 28th prime. prime(28)-3*28= 107-84= 23: prime(28)+3*28= 107+84= 191: 23 and 191 both are primes.
a(9)= 173 which is 40th prime. prime(40)-3*40= 173-120= 53: prime(40)+3*40= 173+120= 293: 53 and 293 both are primes.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..5200

Crossrefs

Cf. A061068 (primes: prime(m) plus its subscript).

Cf. A064402 (numbers n: prime(n)+n is prime).

Cf. A231232 (primes p : p+2*k is also primes).

Cf. A231383 (primes p : p+3*k is also primes).

Programs

Maple

KD := proc() local a,b,d;  a:= ithprime(n); b:= abs(a-3*n);d:=(a+3*n); if isprime(b) and  isprime(d) then RETURN (a); fi; end: seq(KD(), n=1..500);