

A112528


Number of representations of nth prime of the form p1*p2+p3, where p1, p2 and p3 are primes, not necessarily all distinct.


2



0, 0, 0, 1, 3, 2, 5, 2, 4, 4, 2, 5, 6, 4, 4, 6, 4, 3, 6, 5, 4, 6, 4, 8, 7, 6, 5, 6, 6, 9, 6, 7, 8, 5, 8, 6, 7, 10, 5, 9, 8, 6, 6, 7, 10, 7, 9, 9, 6, 9, 12, 11, 7, 8, 11, 8, 11, 8, 11, 12, 9, 11, 13, 9, 10, 14, 13, 13, 7, 9, 12, 12, 12, 14, 11, 11, 15, 13, 15, 12, 13, 9, 12, 12, 13, 14, 13, 14, 13
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OFFSET

1,5


COMMENTS



LINKS



EXAMPLE

No solutions for 2,3,5;
7=2*2+3, 11=2*2+7=2*3+5=3*3+2, 13=2*3+7=2*5+3, 17=2*2+13=2*3+11=2*5+7=2*7+3=3*5+2,
19=2*3+13, 23=2*2+19=2*3+17=2*5+13=3*7+2, 29=2*3+23=2*5+19=2*11+7=2*13+3,
31=2*7+17=2*13+5, ...


MATHEMATICA

Table[Function[q, Length@ DeleteCases[#, s_ /; Length@s != 3] &@ Map[Flatten[ FactorInteger[#] /. {{p_, e_} /; p > 1 :> ConstantArray[p, e], {1, 1} > 1}] &, Select[IntegerPartitions[q, {2}], And[! MemberQ[#, 1], Total@ Boole@ PrimeQ@ # == 1] &]]]@ Prime@ n, {n, 89}] (* Michael De Vlieger, May 01 2017 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



