A076304 Numbers n such that n^2 is a sum of three successive primes.

7, 11, 29, 31, 43, 151, 157, 191, 209, 217, 221, 263, 311, 359, 367, 407, 493, 533, 563, 565, 637, 781, 815, 823, 841, 859, 881, 929, 959, 997, 1013, 1019, 1021, 1087, 1199, 1211, 1297, 1353, 1471, 1573, 1613, 1683, 1685, 1733, 1735, 1739, 1751, 1761, 1769

Offset

1,1

Links

Zak Seidov, Table of n, a(n) for n = 1..255

Formula

a(n) = sqrt(prime(i) + prime(i+1) + prime(i+2)) where i = A076305(n). [Corrected by M. F. Hasler, Jan 03 2020]

Example

7 is in this sequence because 7^2 = 49 = p(6) + p(7) + p(8) = 13 + 17 + 19.

Mathematica

Select[Table[Sqrt[Sum[Prime[k], {k, n, n + 2}]], {n, 100000}], IntegerQ] (* Ray Chandler, Sep 29 2006 *)
Select[Sqrt[#]&/@(Total/@Partition[Prime[Range[90000]], 3, 1]), IntegerQ]  (* Harvey P. Dale, Feb 23 2011 *)

Prog

(PARI) is(n, p=precprime(n^2/3), q=nextprime(p+1), t=n^2-p-q)=isprime(t) && t==if(t>q, nextprime(q+1), precprime(p-1)) \\ Charles R Greathouse IV, May 26 2013; edited by M. F. Hasler, Jan 03 2020
(PARI) A76304=[7]; apply( A076304(n)={if(n>#A76304, my(i=#A76304, N=A76304[i]); A76304=concat(A76304, vector(n-i, i, until( is(N+=2), ); N))); A76304[n]}, [1..99]) \\ M. F. Hasler, Jan 03 2020

Crossrefs

Cf. A206279 (smallest of the 3 primes), A076305 (index of that prime), A080665 (squares = sums), A122560 (subsequence of primes).

Sequence in context: A067006 A136020 A356467 * A122560 A136338 A193867

Adjacent sequences: A076301 A076302 A076303 * A076305 A076306 A076307

Keyword

nonn,easy

Author

Zak Seidov, Oct 05 2002

Status

approved