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 A144294 Let k = n-th nonsquare = A000037(n); then a(n) = smallest prime p such that k is not a square mod p. 7
 3, 5, 3, 7, 5, 3, 7, 3, 5, 5, 3, 13, 3, 5, 7, 3, 11, 5, 3, 7, 3, 5, 5, 3, 11, 7, 3, 5, 7, 3, 5, 3, 11, 7, 3, 5, 5, 3, 7, 11, 3, 5, 3, 11, 5, 3, 7, 7, 3, 5, 5, 3, 13, 7, 3, 5, 3, 7, 5, 3, 7, 13, 3, 5, 5, 3, 7, 7, 3, 5, 11, 3, 5, 3, 11, 11, 3, 5, 5, 3, 7, 17, 3, 5, 7, 3, 7, 5, 3, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS In a posting to the Number Theory List, Oct 15 2008, Kurt Foster remarks that a positive integer M is a square iff M is a quadratic residue mod p for every prime p which does not divide M. He then asks how fast the present sequence grows. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 MAPLE with(numtheory); f:=proc(n) local M, i, j, k; M:=100000; for i from 2 to M do if legendre(n, ithprime(i)) = -1 then RETURN(ithprime(i)); fi; od; -1; end; PROG (PARI) a(n)=my(k=n+(sqrtint(4*n)+1)\2); forprime(p=2, , if(!issquare(Mod(k, p)), return(p))) \\ Charles R Greathouse IV, Aug 28 2016 CROSSREFS For records see A144295, A144296. See A092419 for another version. Sequence in context: A075572 A089992 A074593 * A255313 A305883 A154800 Adjacent sequences:  A144291 A144292 A144293 * A144295 A144296 A144297 KEYWORD nonn AUTHOR N. J. A. Sloane, Dec 03 2008 STATUS approved

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Last modified May 16 21:28 EDT 2021. Contains 343951 sequences. (Running on oeis4.)