A127270 Primes prime(k) such that the sum of the composites between prime(k) and prime(k+2) is prime.

19, 79, 229, 271, 349, 359, 373, 677, 733, 743, 751, 797, 937, 1231, 1279, 1459, 1489, 1549, 1733, 1789, 1801, 1973, 1979, 2069, 2539, 2693, 2777, 2791, 2837, 2857, 3061, 3083, 3191, 3329, 3557, 3559, 3659, 3691, 3719, 3919, 3929, 3989, 4129, 4283, 4447

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Example

The composites between prime(8) = 19 and prime(10) = 29 are 20, 21, 22, 24, 25, 26, 27, 28. Their sum 193 is prime, hence prime(8) = 19 is a term.

Mathematica

Do[p = Prime[n]; If[PrimeQ[Apply[Plus, Select[Table[i, {i, p + 1, Prime[n + 2] - 1}], Not[PrimeQ[ # ]] &]]], Print[p]], {n, 1, 1000}] (* Michael Taktikos, Apr 01 2007 *)

Prog

(Magma) [ p: p in [ NthPrime(k): k in [1..650] ] | IsPrime(&+[ c: c in [p+1..NextPrime(NextPrime(p))-1] ] - NextPrime(p)) ]; /* Klaus Brockhaus, Mar 29 2007 */

Crossrefs

Sequence in context: A158491 A201783 A139941 * A053665 A050522 A366965

Adjacent sequences: A127267 A127268 A127269 * A127271 A127272 A127273

Keyword

nonn

Author

J. M. Bergot, Mar 27 2007

Extensions

Edited and extended by Klaus Brockhaus, Mar 29 2007

Status

approved