A089793 a(n) = the first prime in the earliest chain of 2n+1 consecutive primes whose sum is prime.

2, 5, 5, 17, 3, 5, 29, 3, 3, 11, 7, 7, 5, 7, 13, 13, 7, 5, 5, 13, 7, 7, 7, 7, 11, 17, 3, 3, 97, 29, 3, 13, 3, 19, 19, 3, 5, 3, 23, 7, 11, 53, 31, 89, 53, 19, 11, 3, 17, 23, 83, 11, 5, 47, 37, 5, 17, 3, 3, 29, 23, 5, 5, 5, 59, 7, 7, 31, 3, 67, 3, 3, 89, 71, 31

Offset: 0

Author

Joseph L. Pe, Jan 09 2004

Keywords

• nonn

Comments

In general (except possibly when it begins with 2), the sum of an even number of consecutive primes is even - hence the restriction to odd chain lengths.

Examples

			17 is the first prime in the chain 17, 19, 23, 29, 31, 37, 41, which is the earliest chain of 2 * 3 + 1 = 7 consecutive primes whose sum, 197, is prime. Hence a(3) = 17.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A070934, A215235, A180950, A226380.

Programs

Mathematica

With[{prs=Prime[Range[1000]]},First[#]&/@Flatten[Table[Select[ Partition[ prs,2n+1,1],PrimeQ[Total[#]]&,1],{n,0,80}],1]] (* Harvey P. Dale, Jun 21 2013 *)