A213174 -id:A213174 - cp's OEIS frontend

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

Robert G. Wilson v, Jun 08 2017

nonn

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

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

Cf. A213174.

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]

A288172 a(n) = smallest number that is the sum of 2n - 1, 2n + 1, and 2n + 3 consecutive primes.

Original entry on oeis.org

83, 311, 55813, 42161, 42161, 714295, 113469, 5539053, 20919, 1439643, 7134703, 13432571, 3337639, 6082489, 25241217, 25241217, 2389687, 54309171, 4142423, 63388405, 21570897, 15843991, 62196365, 233917295, 11679841, 96905683, 229821375, 460000131, 125571943

Offset: 1

Zak Seidov, Jun 06 2017

nonn

			n=1: 83 = A000040(23) = A034961(9) = A034964(5) = 23+29+31 = 11+13+17+19+23.
n=20: 63388405 is the sum of 39, 41 and 43 consecutive primes, A000040(122889)+...+A000040(122889+38) = A000040(117360)+...+A000040(122889+40) = A000040(112314)+...+A000040(112314+42).

Cf. A213174.

More terms from Giovanni Resta, Jun 13 2017

cp's OEIS Frontend

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

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A288172 a(n) = smallest number that is the sum of 2n - 1, 2n + 1, and 2n + 3 consecutive primes.

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