A082603 a(n) is the first prime greater than a(n-1) such that a(n)*a(n-1)+2 is a prime, with a(1)=3.

3, 5, 7, 11, 19, 23, 37, 47, 73, 227, 241, 251, 271, 317, 367, 563, 607, 641, 727, 761, 829, 1091, 1117, 1223, 1249, 1451, 1579, 1601, 1627, 1721, 1741, 1787, 1873, 1877, 1933, 1973, 2017, 2087, 2137, 2153, 2287, 2351, 2521, 2687, 2707, 2741, 2851, 3041, 3121, 3137, 3181, 3191, 3361, 3371, 3457, 3461, 3541, 3557, 3607, 3701, 3877, 3881, 3907, 3947

Offset: 1

Author

Jon Perry, May 23 2003

Keywords

• easy
• nonn

Examples

			a(3)=7, as 3 + 2 = 5, 3*5 + 2 = 17, 5*7 + 2 = 37, etc.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A039726, A082603, A096177.

Programs

Mathematica

f[s_List] := Block[{p = pp = s[[-1]]}, While[p = NextPrime@p; !PrimeQ[ p*pp + 2],]; Append[s, p]]; Nest[f, {3}, 63] (* Robert G. Wilson v, Nov 08 2010 *)
fpg[p1_]:=Module[{p2=NextPrime[p1]},While[!PrimeQ[p1 p2+2],p2=NextPrime[ p2]];p2]; NestList[fpg,3,70] (* Harvey P. Dale, May 31 2021 *)

PARI

{ vp=vector(20); vp[1]=3; vc=1; vpt=3; print1(3","); for (vc=2,20, forprime (p=vp[vc-1]+1,10000, if (isprime(p*vp[vc-1]+2),vp[vc]=p;vpt*=p; print1(vp[vc]","); break))) }

PARI

{v=3;print1(3",");forprime(p=5,10000,vp=v*p;if(isprime(vp+2),v=vp;print1(p",")))} \\ Zak Seidov, Nov 07 2010

Extensions

Definition and example corrected to match the sequence and PARI programming, two cross references added, and sequence extended by Robert G. Wilson v, Nov 08 2010