

A230443


Number of decompositions of 2n into a sum of two primes p2 >= p1 such that the number of runs in binary expansion of p2p1 is less than or equal to 4


3



1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 4, 4, 2, 3, 4, 3, 4, 5, 4, 2, 5, 3, 4, 6, 3, 4, 6, 2, 5, 6, 5, 4, 7, 3, 5, 7, 5, 4, 9, 3, 4, 6, 3, 5, 8, 3, 6, 7, 5, 5, 10, 4, 5, 8, 3, 3, 10, 2, 6, 7, 6, 3, 8, 7, 7, 10, 6, 5, 12, 3, 7, 10, 5, 5, 10, 1, 6, 10, 7, 4
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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

n=2, 2n=4, 4=2+2, 22=0, A005811(0)=1 < 4, only one decomposition, so a(2)=1;
...
n=5, 2n=10, 10=5+5=3+7, 55=0, A005811(0)=1<4, 73=4, A005811(4)=2<4, so a(5)=2;
...
n=26, 2n=52, 52=5+47=11+41=23+29. 475=42, A005811(42)=6>4 [X]; 4111=30, A005811(30)=2<4 [v]; 2923=6, A005811(6)=2<4 [v]; so a(26)=2.


MATHEMATICA

Table[ev=2*seed; ct=0; cp1=seed1; While[cp1=NextPrime[cp1]; cp1<ev, cp2=evcp1; If[PrimeQ[cp2], test=cp1cp2; rank=Length[Length/@Split[IntegerDigits[test, 2]]]; If
[rank<=4, ct++]]]; ct, {seed, 2, 100}]


CROSSREFS

Cf. A002372, A005811
Sequence in context: A230197 A094570 A225638 * A254610 A002375 A045917
Adjacent sequences: A230440 A230441 A230442 * A230444 A230445 A230446


KEYWORD

nonn,base,easy


AUTHOR

Lei Zhou, Oct 18 2013


STATUS

approved



