A144294 Let k = n-th nonsquare = A000037(n); then a(n) = smallest prime p such that k is not a square mod p.
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
Offset: 1
Keywords
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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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;
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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
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Python
from math import isqrt from sympy.ntheory import nextprime, legendre_symbol def A144294(n): k, p = n+(m:=isqrt(n))+(n>=m*(m+1)+1), 2 while (p:=nextprime(p)): if legendre_symbol(k,p)==-1: return p # Chai Wah Wu, Oct 20 2024
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