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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = sqrt(prime(n) + prime(n+1) + prime(n+2)) where n is in A076305.

LINKS

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

EXAMPLE

7 is OK 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) for(n=1, 1e4, p=precprime(n^2/3); q=nextprime(p+1); if(isprime(t=n^2-p-q) && t==if(t>q, nextprime(q+1), precprime(p-1)), print1(n", "))) \\ Charles R Greathouse IV, May 26 2013

CROSSREFS

Cf. A076305, A122560.

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

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Last modified May 26 09:06 EDT 2017. Contains 287093 sequences.