

A206279


Smallest of three consecutive primes whose sum is a square.


13



13, 37, 277, 313, 613, 7591, 8209, 12157, 14557, 15679, 16267, 23053, 32233, 42953, 44887, 55213, 81013, 94687, 105649, 106397, 135241, 203317, 221401, 225769, 235747, 245941, 258707, 287671, 306541, 331333, 342049, 346111, 347443, 393853, 479191, 488827
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OFFSET

1,1


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


FORMULA

a(n)=A000040(A076305(n)).  Zak Seidov, Apr 07 2017


EXAMPLE

a(4) = 313. The next two primes are 317 and 331, and 313 + 317 + 331 = 961 = 31^2.


MATHEMATICA

Transpose[Select[Partition[Prime[Range[50000]], 3, 1], IntegerQ[ Sqrt[ Total[#]]]&]][[1]]


PROG

(PARI) p=2; q=3; forprime(r=5, 1e9, if(issquare(p+q+r), print1(p", ")); p=q; q=r) \\ Charles R Greathouse IV, Aug 28 2013


CROSSREFS

Cf. A000040, A061275, A076305, A206280, A206281.
Sequence in context: A090042 A266882 A078952 * A130621 A309594 A098265
Adjacent sequences: A206276 A206277 A206278 * A206280 A206281 A206282


KEYWORD

nonn


AUTHOR

Harvey P. Dale, Feb 05 2012


STATUS

approved



