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A181902
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Numbers k such that the k-th triangular number is prime or the arithmetic mean of 2 successive primes.
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2
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2, 3, 5, 6, 9, 14, 15, 21, 24, 26, 30, 38, 39, 41, 48, 53, 54, 78, 80, 81, 87, 89, 92, 104, 116, 117, 119, 121, 122, 125, 126, 146, 149, 150, 153, 156, 158, 164, 165, 170, 171, 185, 186, 194, 206, 210, 218, 245, 248, 252, 255, 258, 270, 281, 285, 290, 296, 297
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OFFSET
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1,1
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LINKS
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EXAMPLE
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2 is a term because 2*(2+1)/2 = 3 is prime,
3 is a term because 3*(3+1)/2 = (5+7)/2,
5 is a term because 5*(5+1)/2 = (13+17)/2.
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MATHEMATICA
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a = {2}; For[n = 1, n < 320, n++, t = n*(n + 1)/2;
If[t == (NextPrime[t] + NextPrime[t, -1])/2, AppendTo[a, n],
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PROG
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(Magma) [2] cat [n: n in [3..320] | 2*t eq PreviousPrime(t)+NextPrime(t) where t is n*(n+1) div 2]; // Bruno Berselli, Apr 04 2012
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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