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A105720
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Triangular matchstick numbers in the class of prime numbers: sum of n-th and next n primes.
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7
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5, 15, 36, 67, 112, 169, 240, 323, 424, 539, 662, 803, 964, 1133, 1312, 1523, 1746, 1987, 2246, 2519, 2808, 3119, 3436, 3787, 4154, 4529, 4920, 5337, 5770, 6219, 6682, 7173, 7672, 8203, 8760, 9323, 9912, 10517, 11140, 11783, 12450, 13135, 13836
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OFFSET
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1,1
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COMMENTS
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Terms are squares at only(?) three values of n = 3, 6, 4072: corresponding terms are 6^2, 13^2, and 15735^2.
Terms are prime at many values of n; at n = 1, 4, 16, 18, 22, 36, 40, 44, 52 they are 5, 67, 1523, 1987, 3119, 9323, 11783, 14551, 21019.
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LINKS
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FORMULA
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a(n) = p(n) + p(n+1) + ... + p(2n-1) + p(2n), where p(k)=k-th prime.
a(1)=5; for n > 1, a(n) = a(n-1) - prime(n-1) + prime(2*n-1) + prime(2*n). - Zak Seidov, Oct 18 2009
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MATHEMATICA
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a[n_]:=Plus@@Prime[Range[n, 2n]]
a=5; s={5}; Do[a=a-Prime[n]+Prime[2n+1]+Prime[2n+2]; AppendTo[s, a], {n, 10^5}]; (* Zak Seidov, Oct 18 2009 *)
Table[Total[Prime[Range[n, 2n]]], {n, 50}] (* Harvey P. Dale, Jun 10 2014 *)
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PROG
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(Magma) [ &+[ NthPrime(n+i): i in [0..n] ]: n in [1..50] ]; // Bruno Berselli, Jul 08 2011
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CROSSREFS
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Cf. A045943 (triangular matchstick numbers: 3*n*(n+1)/2).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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