A288340 a(n) is the smallest prime that is the sum of both 2n-1 and 2n+1 consecutive primes.

23, 83, 311, 401, 1367, 3617, 863, 5683, 1523, 153113, 90011, 10949, 7901, 155671, 11131, 117977, 14699, 252079, 58369, 132749, 203293, 641867, 116257, 607093, 78791, 46471, 927049, 340601, 1485541, 521897, 99149, 771889, 2153993, 227869, 2349251, 4762213, 56099, 3232093, 944003, 1006781

Offset: 1

Author

Robert G. Wilson v, Jun 08 2017

Keywords

• nonn

Comments

Inspired by A213174.

Records: 23, 83, 311, 401, 1367, 3617, 5683, 153113, 155671, 252079, 641867, 927049, 1485541, 2153993, 2349251, 4762213, ..., . - Robert G. Wilson v, Jun 11 2017

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 812 terms from Robert G. Wilson v)

Crossrefs

Cf. A213174.

Programs

Mathematica

pr = Prime@ Range@ 25000; f[n_] := Select[ Intersection[Plus @@@ Partition[pr, 2n -1, 1], Plus @@@ Partition[pr, 2n +1, 1]], PrimeQ][[1]]; Array[f, 40] (* or *)
f[n_] := Block[{a = Prime@ Range[2, 2n], p = Prime[2n +1], b = Prime@ Range[2, 2n +2], q = Prime[2n +3]}, While[aa = Plus @@ a; bb = Plus @@ b; aa != bb || ! PrimeQ@ aa, If[aa < bb, a = Join[Rest@ a, {p}]; p = NextPrime@ p, b = Join[Rest@ b, {q}]; q = NextPrime@ q]]; Plus @@ a]; Array[f, 40]