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 A306678 Number of distinct triangles with prime sides and largest side = prime(n). 4
 1, 3, 4, 6, 7, 11, 13, 18, 21, 22, 29, 30, 37, 46, 53, 56, 60, 71, 75, 87, 101, 105, 118, 124, 123, 139, 157, 173, 193, 209, 186, 207, 219, 244, 241, 264, 277, 291, 318, 329, 344, 371, 373, 405, 433, 465, 447, 440, 474, 511, 545, 563, 597, 602, 623, 645 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA a(n) = A306676(n) + A306677(n). EXAMPLE For n=1, there is 1 triangle: {2, 2, 2}, with largest side prime(1) = 2. For n=2, there are 3 triangles: {2, 2, 3}, {2, 3, 3}, {3, 3, 3}, with largest side prime(2) = 3. For n=4, there are 6 triangles :{2, 7, 7}, {3, 5, 7}, {3, 7, 7}, {5, 5, 7}, {5, 7, 7}, {7, 7, 7}, with largest side prime(4) = 7. Total = 6 = a(4). For n=5, largest side = prime(n) = 11. Triangles are {{2, 11, 11}, {3, 11, 11}, {5, 7, 11}, {5, 11, 11}, {7, 7, 11}, {7, 11, 11}, {11, 11, 11}}. Total = 7 = a(5). MAPLE #nType=1 for acute triangles, nType=2 for obtuse triangles #nType=0 for both triangles CountPrimeTriangles := proc (n, nType := 1)   local aa, oo, j, k, sg, a, b, c, tt, lAcute;   aa := {}; oo := {};   a := ithprime(n);   for j from n by -1 to 1 do     b := ithprime(j);     for k from j by -1 to 1 do       c := ithprime(k);       if a < b+c and abs(b-c) < a and b < c+a and abs(c-a) < b and c < a+b and abs(a-b) < c then         lAcute := evalb(0 < b^2+c^2-a^2);         tt := sort([a, b, c]);         if lAcute then aa := {op(aa), tt} else oo := {op(oo), tt} end if       end if     end do   end do;   return sort(`if`(nType = 1, aa, `if`(nType = 2, oo, `union`(aa, oo)))) end proc: CROSSREFS Cf. A306673, A306674, A306676, A306677. Sequence in context: A011975 A202112 A079249 * A075434 A085253 A207525 Adjacent sequences:  A306675 A306676 A306677 * A306679 A306680 A306681 KEYWORD nonn AUTHOR César Eliud Lozada, Mar 04 2019 STATUS approved

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Last modified February 21 04:39 EST 2020. Contains 332086 sequences. (Running on oeis4.)