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A061784 Number of sums prime(i) + prime(j) that occur more than once for 1<=i<=j<=n, prime(k) = k-th prime. 2
0, 0, 0, 1, 2, 4, 7, 11, 16, 22, 27, 34, 41, 51, 61, 73, 86, 96, 110, 124, 140, 158, 175, 193, 211, 231, 252, 275, 299, 325, 348, 374, 401, 427, 456, 486, 516, 549, 581, 615, 650, 684, 722, 759, 798, 839, 879, 921, 961, 1005, 1048, 1095, 1142, 1189, 1238 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..55.

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)-17=4.

MATHEMATICA

f[x_] := Prime[x] t1=Table[Length[Union[Flatten[Table[f[u]+f[w], {w, 1, m}, {u, 1, m}]]]], {m, 1, 75}] t=Table[(w*(w+1)/2)-Part[t1, w], {w, 1, 75}]

CROSSREFS

Cf. A000217, A061781.

Sequence in context: A024673 A002789 A083204 * A005311 A296202 A126613

Adjacent sequences:  A061781 A061782 A061783 * A061785 A061786 A061787

KEYWORD

nonn

AUTHOR

Labos Elemer, Jun 22 2001

STATUS

approved

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Last modified August 9 13:50 EDT 2020. Contains 336323 sequences. (Running on oeis4.)