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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A039726, A082603, A096177.

Sequence in context: A138536 A093929 A144427 * A362250 A161420 A071997

Adjacent sequences: A082600 A082601 A082602 * A082604 A082605 A082606

Keyword

easy,nonn

Author

Jon Perry, May 23 2003

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

Status

approved