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A138225
Number of pairs (p,q) of primes with p < q < prime(n), p + q > prime(n), q + prime(n) > p and prime(n) + p > q.
1
0, 0, 0, 1, 1, 3, 4, 7, 9, 9, 14, 14, 20, 27, 33, 34, 37, 46, 49, 59, 71, 74, 86, 91, 89, 103, 119, 134, 152, 166, 143, 162, 173, 196, 193, 214, 225, 238, 264, 273, 287, 312, 312, 342, 369, 399, 381, 374, 407, 442, 474, 490, 522, 525, 545, 566, 587, 623, 646, 683
OFFSET
1,6
COMMENTS
Beginning with a(3)=0, the sequence is an application of the triangle inequality for non-degenerate scalene triangles with longest side = prime(n), middle side = q, and shortest side = p. To wit: the number of such triangles that can be formed with longest side = prime(n). - Gil Broussard, Jun 15 2022
EXAMPLE
A000040(7)=17: a(7) = #((7,11),(5,13),(7,13),(11,13)) = 4.
CROSSREFS
Cf. A000040, A138226 (partial sums).
Sequence in context: A075773 A324495 A087276 * A114889 A174659 A242423
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 06 2008
STATUS
approved