A064466 a(0) = 6 and a(n) = Min { m > a(n-1) | both a(n-1) - p and m - p are prime for some prime p } for n > 0.

6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 72, 74, 76, 78, 80, 84, 86, 88, 90, 92, 94, 96, 98, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 126, 128, 132, 134, 136, 138, 140, 142

Offset: 0

Author

Reinhard Zumkeller, Oct 02 2001

Keywords

• nonn

Comments

The initially very frequent case a(k+1) = a(k) + 2 means that there is a twin prime (q, q + 2) with a(k+1) = p + (q + 2) and a(k) = p + q. This might illustrate a certain coherence of two famous conjectures: Goldbach and twin primes.

Examples

			a(12) = 30 = 13 + 17: a(13) = 30 + 2 = 32 = 13 + 19 (common prime = 13). No common prime exists in Goldbach decompositions for a(16) = 38 and 40, so 40 <> a(17) = 42; a(16) = 38 = 7 + 31 = 19 + 19, 40 = 3 + 37 = 11 + 29 = 17 + 23, a(17) = 42 = 11 + 31 (for 38 and 42 common prime = 31); A064634(1) = 16, A064635(1) = 40 = 2 + 38 = 2 + a(A064634(1)).
		

Crossrefs

Cf. A001359, A002373, A064634, A064635.