A216004 Primes that are the sum of 2001 consecutive primes.

16344247, 16588633, 16711217, 17416457, 17700139, 17806721, 17860039, 17895613, 18091313, 18144727, 18483739, 18573209, 18698791, 19040773, 19384609, 19529849, 19620719, 19748129, 19784543, 19802759, 20421971, 20476777, 20531593, 20806141, 21283169, 21356563

Offset: 1

Author

Syed Iddi Hasan, Aug 30 2012

Keywords

• nonn

Comments

Corresponding initial terms of 2001-tuples: 7, 61, 97, 313, 419, 449, 463, 479, 563, 577, 691, 733, 773, 911, 1039, 1093, 1123, 1187, 1201, 1213, 1459, 1483, 1493, 1607. The indices of these primes: 4, 18, 25, 65, 81, 87, 90, 92, 103, 106, 125, 130, 137, 156, 175, 183, 188, 195, 197, 198, 232, 235, 238, 253. - Zak Seidov, Feb 27 2013

Examples

			a(1) = sum(prime(k), k = 4..2004),  a(2) = sum(prime(k), k = 18..2018),... - _Zak Seidov_, Feb 27 2013
		

Links

• Syed Iddi Hasan, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A070934, A082244, A215991.

Programs

Mathematica

m = 2001; a = 2; b = Prime[m]; s = Sum[Prime[k], {k, m}]; Reap[Do[If[PrimeQ[s], Sow[s]]; b = NextPrime[b]; s = s - a + b; a = NextPrime[a], {m}]][[2, 1]] (* Zak Seidov, Feb 27 2013 *)
Select[Total/@Partition[Prime[Range[2500]],2001,1],PrimeQ] (* Harvey P. Dale, Mar 13 2018 *)