OFFSET
0,1
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.
EXAMPLE
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 02 2001
STATUS
approved