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A225924
Number of solutions to 2n - 1 = (p1*p2 + p3)/2, where p1, p2, and p3 are prime numbers less than 2n-1.
1
0, 1, 0, 1, 1, 1, 2, 1, 1, 4, 3, 3, 2, 3, 4, 6, 3, 4, 4, 3, 4, 4, 4, 6, 9, 5, 6, 5, 5, 6, 7, 7, 7, 8, 8, 5, 9, 7, 7, 10, 10, 10, 8, 10, 7, 11, 8, 11, 9, 8, 10, 10, 6, 11, 12, 15, 14, 14, 11, 12, 13, 11, 12, 11, 13, 12, 14, 12, 11, 13, 13, 11, 14, 13, 12, 12
OFFSET
1,7
COMMENTS
It is hypothesized that a(n)>0 for all n > 3.
EXAMPLE
When n=1, 2n-1=1, which cannot be written into form (p1*p2+p3)/2, so a(1)=0;
When n=2, 2n-1=3, 3=(2*2+2)/2, and this is the only way, so a(2)=1;
...
When n=7, 2n-1=13, 13=(3*7+5)/2=(3*5+11)/2, so a(7)=2.
MATHEMATICA
Table[p=NextPrime[i, -1]; ct=0; While[cd=2*i-p; If[fct=Transpose[FactorInteger[cd]]; lf=Length[fct[[1]]]; lf==2, If[fct[[2, 1]]*fct[[2, 2]]==1, If[fct[[1, 2]]<i, ct++]], If[lf==1, If[fct[[2, 1]]==2, If[fct[[1, 1]]<i, ct++]]]]; p=NextPrime[p, -1]; p>2]; ct, {i, 1, 151, 2}]
CROSSREFS
Sequence in context: A262357 A112744 A249577 * A078015 A366781 A240769
KEYWORD
nonn,easy
AUTHOR
Lei Zhou, May 20 2013
STATUS
approved