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%I #10 Sep 08 2022 08:46:02
%S 107,113,383,567,601,951,1005,1059,1169,1269,1313,1343,1415,1641,1719,
%T 1759,1823,2237,2315,2323,2505,2605,2737,2743,2801,2881,2913,3351,
%U 3355,3405,3583
%N n^2 is a sum of 11 consecutive primes.
%C Initial primes of the sets of 11 consecutive primes are
%C 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
%C and their indices are
%C 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
%e 107^2 = 11449 = prime(170) + ... + prime(180) = 1013 + ... + 1069.
%t Select[Sqrt[Total /@ Partition[Prime[Range[100000]], 11, 1]], IntegerQ]
%o (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
%K nonn
%O 1,1
%A _Zak Seidov_, Mar 05 2013