OFFSET
2,4
COMMENTS
1. This is a tightly intensified version of Goldbach conjecture.
It is hypothesized that except for n=1402 and 27242, all other terms for n > 1 are greater than zero. Sequence tested up to 1 million without other zero elements.
2. The definition of "the number of runs in binary expansion of k" is from A005811.
3. The first difference of this sequence to A002375 is on a(26).
LINKS
Lei Zhou, Table of n, a(n) for n = 2..10000
EXAMPLE
MATHEMATICA
Table[ev=2*seed; ct=0; cp1=seed-1; While[cp1=NextPrime[cp1]; cp1<ev, cp2=ev-cp1; If[PrimeQ[cp2], test=cp1-cp2; rank=Length[Length/@Split[IntegerDigits[test, 2]]]; If
[rank<=4, ct++]]]; ct, {seed, 2, 100}]
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Lei Zhou, Oct 18 2013
STATUS
approved