

A076304


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


13



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
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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^2pq)=isprime(t) && t==if(t>q, nextprime(q+1), precprime(p1)) \\ 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(ni, 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: A158807 A067006 A136020 * A122560 A136338 A193867
Adjacent sequences: A076301 A076302 A076303 * A076305 A076306 A076307


KEYWORD

nonn,easy


AUTHOR

Zak Seidov, Oct 05 2002


STATUS

approved



