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A072849
Prime(a(n)) + ... + prime(a(n)+3) is a square = A051395(n)^2.
9
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
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
KEYWORD
easy,nonn
AUTHOR
Zak Seidov, Jun 21 2003
EXTENSIONS
Definition corrected by Zak Seidov, Dec 13 2014
STATUS
approved