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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.
1
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
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
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