

A061781


Number of distinct sums p(i) + p(j) for 1<=i<=j<=n, p(k) = kth prime.


4



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
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OFFSET

1,2


LINKS

Zak Seidov, Table of n, a(n) for n = 1..10000


FORMULA

f[x_] := Prime[x] Table[Length[Union[Flatten[Table[f[u]+f[w], {w, 1, m}, {u, 1, m}]]]], {m, 1, 75}]


EXAMPLE

If {p+q} sums are produced by adding 2 terms of an S set consisting of n different entries, then at least 1, at most n(n+1)/2=A000217(n) distinct values can be obtained. The set of first n primes gives results falling between these two extremes. E.g. S={2,3,5,7,11,13} provides 17 different sums of two, not necessarily different primes: {4,5,6,7,8,9,10,12,13,14,15,16,18,20,22,24,26}. Four sums arise more than once:10=3+7=5+5,14=3+11=7+7, 16=3+13=5+11,18=5+13=7+11. Thus a(6)=(6*7/2)4=17.


CROSSREFS

Cf. A000217, A061784.
Sequence in context: A325228 A278449 A006590 * A123753 A124288 A256966
Adjacent sequences: A061778 A061779 A061780 * A061782 A061783 A061784


KEYWORD

nonn


AUTHOR

Labos Elemer, Jun 22 2001


STATUS

approved



