A237057 a(n) = smallest prime > a(n-1) such that a(n)+4n is also prime.

2, 3, 5, 7, 13, 17, 19, 31, 41, 43, 61, 83, 89, 97, 101, 103, 109, 113, 127, 151, 191, 193, 223, 239, 241, 283, 293, 311, 331, 347, 359, 367, 419, 431, 433, 461, 463, 499, 509, 521, 523, 563, 571, 601, 647, 659, 673, 719, 727, 733, 797, 809, 811, 821, 823, 829

Offset: 0

Author

Carmine Suriano, Feb 03 2014

Keywords

• nonn

Comments

Many twin primes belong to the sequence, for example (41, 43) and (191, 193).

Many consecutive primes also appear such as (13, 17) and (83, 89).

Examples

			a(5)=17 since 17+4*5=17+20=37 is prime. 11+4*4=27 is not prime, so 11 is not in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A108184.

Programs

Mathematica

nxt[{n_,p_}]:=Module[{np=NextPrime[p]},While[!PrimeQ[np+4(n+1)],np = NextPrime[ np]];{n+1,np}]; Transpose[NestList[nxt,{0,2},60]][[2]] (* Harvey P. Dale, Feb 26 2015 *)

PARI

a237057(maxp) = {my(a=[2], n=1); forprime(p=3, maxp, if(isprime(p+4*n), n++; a=concat(a, p)));  a} \\ Colin Barker, Feb 12 2014