A227196 - OEIS

%I #25 Jan 11 2023 12:19:41

%S 0,2,2,2,2,2,3,2,3,2,2,2,2,2,3,2,3,2,2,2,2,2,5,2,5,2,2,2,2,2,3,2,3,2,

%T 2,2,2,2,3,2,3,2,2,2,2,2,5,2,7,2,2,2,2,2,3,2,3,2,2,2,2,2,3,2,3,2,2,2,

%U 2,2,7,2,5,2,2,2,2,2,3,2,3,2,2,2,2,2,3

%N a(n) = first i >= 1 for which the Kronecker symbol K(i,n) is not +1 (i.e., is either 0 or -1), 0 if no such i exists.

%C a(1) = 0, because K(i,1) is 1 for all i. After that, A112046 interleaved with A007395.

%C All terms beyond a(1) = 0 are prime numbers. Heuristically a(n) is 2 3/4 of the time, 3 1/6 of the time, 5 1/20 of the time, 7 2/105 of the time, etc. The average value is 2.5738775742512.... - _Charles R Greathouse IV_, Jan 30 2018

%H A.H.M. Smeets, <a href="/A227196/b227196.txt">Table of n, a(n) for n = 1..20163</a> (first 87 terms from Antti Karttunen)

%F A227195(n) = a(n)-1 for all n>=2.

%F a(2n+1) = A112046(n) for all n>0. - _A.H.M. Smeets_ Jan 29 2018

%o (PARI) a(n) = for(k=1,n,if(kronecker(k,n)<1, return(k)))

%o for(n=1,120, print1(a(n),", "))

%Y Bisections: A112046 (for odd terms from 3 onward), A007395 (all even terms).

%Y Cf. A227195, A227197, A227198, A112052.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 06 2013