A213915 n^2 is a sum of 11 consecutive primes.

107, 113, 383, 567, 601, 951, 1005, 1059, 1169, 1269, 1313, 1343, 1415, 1641, 1719, 1759, 1823, 2237, 2315, 2323, 2505, 2605, 2737, 2743, 2801, 2881, 2913, 3351, 3355, 3405, 3583

Offset

1,1

Comments

Initial primes of the sets of 11 consecutive primes are

1013, 1117, 13291, 29179, 32789, 82183, 91771, 101891, 124181, 146347, 156679, 163901, 181967, 244747, 268537, 281233, 301999, 454859, 487111, 490541, 570407, 616843, 680971, 683923, 713183, 754483, 771349, 1020779, 1023227, 1053959, 1166987

and their indices are

170, 187, 1578, 3172, 3516, 8035, 8867, 9757, 11664, 13538, 14409, 15007, 16490, 21614, 23524, 24535, 26165, 38072, 40538, 40807, 46852, 50379, 55135, 55356, 57545, 60580, 61836, 80027, 80212, 82399, 90554

Links

Table of n, a(n) for n=1..31.

Example

107^2 = 11449 = prime(170) + ... + prime(180) = 1013 + ... + 1069.

Mathematica

Select[Sqrt[Total /@ Partition[Prime[Range[100000]], 11, 1]], IntegerQ]

Prog

(Magma) [Isqrt(m): n in [1..10^5] | IsSquare(m) where m is &+[NthPrime(n+i): i in [0..10]]]; // Bruno Berselli, Mar 05 2013

Crossrefs

Sequence in context: A294744 A118774 A033218 * A033258 A095647 A039555

Adjacent sequences: A213912 A213913 A213914 * A213916 A213917 A213918

Keyword

nonn

Author

Zak Seidov, Mar 05 2013

Status

approved