A339709 a(n) is the least even number that has exactly n decompositions as the sum of an odd prime and a semiprime, or 0 if there is no such number.
2, 12, 20, 26, 28, 44, 38, 52, 76, 80, 62, 92
Offset: 0
Examples
a(4) = 28 because we can write 28 = 3+25 = 7+21 = 13+15 = 19+9 where 3, 7, 13 and 19 are odd primes and 25, 21, 15, and 9 are semiprimes, and 28 is the least even number with exactly 4 decompositions of this type.
Links
- Robert Israel, Table of n, a(n) for n = 0 .. 800 (with conjectured a(12)=0).
Crossrefs
Cf. A339708.
Programs
-
Maple
N:= 10000: P:= select(isprime,[seq(i,i=3..N,2)]):S:= sort(select(`<`,[seq(seq(P[i]*P[j],i=1..j),j=1..nops(P))],N)):V:= Vector(N): for p in P do for s in S while p+s<=N do V[p+s]:= V[p+s]+1 od od:R:= Array(0..max(V)):for i from 2 to N by 2 do v:= V[i]; if R[v] = 0 then R[v]:= i fi od:convert(R[1..500],list);
Comments