A072849 Prime(a(n))+...+prime(a(n)+3) is a square = A051395(n)^2.

3, 21, 33, 84, 104, 199, 689, 1848, 1923, 3435, 3795, 3985, 4126, 4742, 5968, 6413, 6495, 7649, 8927, 9906, 16885, 17677, 20474, 20996, 22924, 23923, 36902, 38733, 40347, 40654, 41956, 42601, 43047, 44482, 44920, 51608, 52305, 56706, 66032

Offset

1,1

Comments

Conjecture: this sequence and A064397 are disjoint. That is to say, prime(n) + prime(n+1) and prime(n) + prime(n+1) + prime(n+2) + prime(n+3) cannot be squares at the same time. - Jianing Song, Nov 13 2022

Links

Harvey P. Dale, Table of n, a(n) for n = 1..200

Example

a(1)=3 because prime(3)+prime(4)+prime(5)+prime(6) = 5+7+11+13 = 36 = 6*6.

Mathematica

Flatten[Position[Partition[Prime[Range[70000]], 4, 1], _?(IntegerQ[ Sqrt[ Total[ #]]]&), {1}, Heads->False]] (* Harvey P. Dale, Dec 09 2015 *)

Prog

(PARI) lista(m) = {for (n = 1, m, if (issquare(prime(n) + prime(n+1) + prime(n+2) + prime(n+3)), print1(n, ", ")); ); }  \\ Michel Marcus, Apr 19 2013

Crossrefs

Cf. A051395 (square root of sums), A206280 (primes).

Cf. A064397 (2 primes), A076305 (3 primes), A166255 (70 primes), A166261 (120 primes).

Sequence in context: A006133 A317860 A039766 * A287930 A287799 A089323

Adjacent sequences: A072846 A072847 A072848 * A072850 A072851 A072852

Keyword

easy,nonn

Author

Zak Seidov, Jun 21 2003

Extensions

Definition corrected by Zak Seidov, Dec 13 2014

Status

approved