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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 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: 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 October 26 19:14 EDT 2020. Contains 338027 sequences. (Running on oeis4.)