A072849 - OEIS

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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

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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

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..200 from Harvey P. Dale)

FORMULA

a(n) = A000720(A206280(n)). - Amiram Eldar, Jun 28 2024

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), A000720.

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