A061781 Number of distinct sums p(i) + p(j) for 1<=i<=j<=n, p(k) = k-th prime.
1, 3, 6, 9, 13, 17, 21, 25, 29, 33, 39, 44, 50, 54, 59, 63, 67, 75, 80, 86, 91, 95, 101, 107, 114, 120, 126, 131, 136, 140, 148, 154, 160, 168, 174, 180, 187, 192, 199, 205, 211, 219, 224, 231, 237, 242, 249, 255, 264, 270, 278, 283, 289, 296, 302, 306, 310, 319
Offset: 1
Keywords
Examples
Let P(n) = {2, 3, .., p_n} be the set of the first n primes. Construct S(n) = {p+q : p,q in P}. If every sum p+q were distinct, then |S(n)| would be n*(n+1)/2 = A000217(n). But in reality, for n >= 4, certain sums occur more than once. a(n) = |S(n)|. For example, P(6) = {2, 3, 5, 7, 11, 13} yields S(6) = {4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 20, 22, 24, 26}. Thus, a(6) = 17.
Links
- Zak Seidov, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
f[x_] := Prime[x] Table[Length[Union[Flatten[Table[f[u]+f[w], {w, 1, m}, {u, 1, m}]]]], {m, 1, 75}]