A231432 Primes p such that abs(p - 3*k) is also prime, where p is the k-th prime.

3, 7, 13, 19, 31, 41, 47, 53, 61, 71, 79, 89, 101, 107, 113, 139, 151, 173, 193, 199, 223, 229, 239, 251, 271, 281, 293, 349, 373, 397, 433, 457, 463, 521, 541, 557, 569, 593, 601, 613, 619, 641, 647, 673, 683, 743, 787, 809, 839, 911, 941, 953, 971, 1013, 1049

Offset: 1

Author

K. D. Bajpai, Nov 09 2013

Keywords

• nonn
• easy

Examples

			The first prime, 2, is not a term since |2-3*1| = 1.
The second prime, 3, is a term, since |3-2*3| = 3 is a prime.
a(11) = 79 which is the 22nd prime, prime(22)-3*22 = 79-66 = 13 which is also prime.
a(15) = 113 which is the 30th prime, prime(30)-3*30 = 113-90 = 23 which is also prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..6400

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 prime).

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

Programs

Maple

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

Mathematica

KD = Select[Table[{Prime[n], Prime[n] - 3*n}, {n, 200}], PrimeQ[#[[2]]] &]; Transpose[KD][[1]]
Select[Table[{k,Prime[k]},{k,200}],PrimeQ[Abs[#[[2]]-3#[[1]]]]&][[;;,2]] (* Harvey P. Dale, Jul 14 2024 *)

PARI

k=0;forprime(p=2,1e3,if(isprime(abs(p-k++*3)), print1(p", "))) \\ Charles R Greathouse IV, Mar 11 2014