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A076304 Numbers n such that n^2 is a sum of three successive primes. 14
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
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
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Oct 05 2002
STATUS
approved

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Last modified September 28 23:23 EDT 2023. Contains 365739 sequences. (Running on oeis4.)