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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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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Cf. A045943 Triangular matchstick numbers: sum of n and next n integers; a(n) are full squares at only(?) three values of n = 3, 6, 4072: {6,13,15735}^2;a(n) are primes at many values of for n = 1,4,16,18,22,36,40,44,52,...: 5,67,1523,1987,3119,9323,11783,14551,21019,...
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FORMULA
| a(n)=p(n)+p(n+1)+...+p(2n-1)+p(2n), p(k)=k-th prime
a(1)=5; n>1: a(n)=a(n-1)-prime(n-1)+prime(2*n-1)+prime(2*n). [From Zak Seidov (zakseidov(AT)yahoo.com), Oct 18 2009]
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MATHEMATICA
| 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}]; [From Zak Seidov (zakseidov(AT)yahoo.com), Oct 18 2009]
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PROG
| (MAGMA) [ &+[ NthPrime(n+i): i in [0..n] ]: n in [1..50] ]; // Bruno Berselli, Jul 08 2011
(PARI) a(n)=my(s=0); forprime(p=prime(n), prime(2*n), s+=p); s \\ Charles R Greathouse IV, Jul 08 2011
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CROSSREFS
| Cf. A045943.
Cf. A166619, A166620. [From Zak Seidov (zakseidov(AT)yahoo.com), Oct 18 2009]
Sequence in context: A056413 A032276 A065780 * A174655 A184631 A011933
Adjacent sequences: A105717 A105718 A105719 * A105721 A105722 A105723
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KEYWORD
| nonn
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), May 04 2005
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