A166620 -id:A166620 - cp's OEIS frontend

A105720 Triangular matchstick numbers in the class of prime numbers: sum of n-th and next n primes.

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

Offset: 1

Zak Seidov, May 04 2005

nonn

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.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A045943 (triangular matchstick numbers: 3*n*(n+1)/2).
Cf. A045943.
Cf. A166619, A166620. - Zak Seidov, Oct 18 2009

[ &+[ NthPrime(n+i): i in [0..n] ]: n in [1..50] ];  // Bruno Berselli, Jul 08 2011

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 *)

a(n)=my(s=0);forprime(p=prime(n),prime(2*n),s+=p);s \\ Charles R Greathouse IV, Jul 08 2011

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

A166619 Primes in A105720.

Original entry on oeis.org

5, 67, 1523, 1987, 3119, 9323, 11783, 14551, 21019, 42929, 108191, 177337, 194527, 225227, 244753, 251417, 265123, 301123, 308569, 450503, 507523, 622067, 655351, 772789, 835249, 860891, 900241, 940403, 995611, 1141241, 1171789, 1534727

Offset: 1

Zak Seidov, Oct 18 2009

nonn

Cf. A166620 (Positions of primes in A105720), A105720.

A166708 Squares in A105720.

Original entry on oeis.org

36, 169, 247590225

Offset: 1

Zak Seidov, Oct 18 2009

			36=6^2=A105720(3),
169=13^2=A105720(6),
247590225=15735^2=A105720(4072)
No more terms up to 35746494200563714=A105720(34769014).

Cf. A105720, A166619, A166620.

a=5;Do[a=a-Prime[n]+Prime[2n+1]+Prime[2n+2];If[IntegerQ[Sqrt[a]],Print[{a,n+1 }]],{n,1,10^8}];

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A105720 Triangular matchstick numbers in the class of prime numbers: sum of n-th and next n primes.

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A166619 Primes in A105720.

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A166708 Squares in A105720.

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