A126938 a(1) = 3, a(n) = the smallest prime p > a(n-1) such that (a(n-1)+p)/2 is prime.

3, 7, 19, 43, 79, 127, 151, 163, 199, 223, 331, 367, 379, 439, 487, 607, 619, 643, 739, 883, 991, 1051, 1087, 1171, 1231, 1327, 1471, 1627, 1699, 1747, 1759, 1987, 1999, 2179, 2383, 2551, 2683, 2731, 2767, 3067, 3259, 3343, 3571, 3643, 3739, 3847, 3907

Offset: 1

Author

Zak Seidov, Mar 18 2007

Keywords

• nonn

Comments

Starting with a(2)=7 all terms are 7 mod 12. - Zak Seidov, Feb 26 2017

Examples

			(3+7)/2=5 prime, (7+19)/2=13 prime, (19+43)/2=31 prime, etc.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A084704, A128653, A128654, A128655.

Programs

Maple

A[1]:= 3: A[2]:= 7:
for n from 3 to 100 do A[n]:= f(A[n-1]) od:
seq(A[i],i=1..100); # Robert Israel, Feb 27 2017

Mathematica

s={3};pn=3;n=PrimePi[pn];Do[Do[p=Prime[i];If[PrimeQ[(pn+p)/2],AppendTo[s,p];pn=p;n=i;Break[]],{i,n+1,10000}],{112}];s
sp[n_]:=Module[{p=NextPrime[n]},While[!PrimeQ[(n+p)/2],p=NextPrime[p]];p]; NestList[sp,3,50] (* Harvey P. Dale, Apr 12 2013 *)

PARI

step(q)=forprime(p=q+1,, if(isprime((p+q)/2), return(p)))
first(n)=my(v=vector(n)); v[1]=3; for(k=2,n, v[k]=step(v[k-1])); v \\ Charles R Greathouse IV, Feb 27 2017