A198519 a(2n-1) is the first unused prime which is the sum of the two preceding terms and such that a(2n) is that sum and it is also an unused prime.

3, 5, 11, 19, 7, 37, 17, 61, 23, 101, 13, 137, 29, 179, 31, 239, 41, 311, 67, 419, 71, 557, 73, 701, 47, 821, 43, 911, 59, 1013, 79, 1151, 53, 1283, 97, 1433, 83, 1613, 127, 1823, 89, 2039, 109, 2237, 113, 2459, 139, 2711, 103, 2953, 107, 3163, 163, 3433, 131, 3727, 149, 4007, 181, 4337, 173, 4691

Offset: 1

Author

Robert G. Wilson v, Dec 21 2012

Keywords

• easy
• nonn

Examples

			a(3) does not equal 7 since 3+5+7 which is 15 is not a prime, but the next prime, 11, meets the criteria.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A073653, A084331, A101595.

Programs

Mathematica

s = {3, 5}; k = 1; While[k < 31, p = s[[-2]] + s[[-1]]; q = 7; While[ !PrimeQ[p + q] || MemberQ[s, q] || MemberQ[s, p + q], q = NextPrime@ q]; AppendTo[s, q]; AppendTo[s, p + q]; k++]; s