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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
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
KEYWORD
nonn
AUTHOR
Harvey P. Dale, Feb 05 2012
STATUS
approved