A227196 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.

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, 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, 2, 2, 7, 2, 5, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3

Offset: 1

Author

Antti Karttunen, Jul 06 2013

Keywords

• nonn

Comments

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

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

Links

• A.H.M. Smeets, Table of n, a(n) for n = 1..20163 (first 87 terms from Antti Karttunen)

Crossrefs

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

Cf. A227195, A227197, A227198, A112052.

Programs

PARI

a(n) = for(k=1,n,if(kronecker(k,n)<1, return(k)))
for(n=1,120, print1(a(n),", "))

Formula

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

a(2n+1) = A112046(n) for all n>0. - A.H.M. Smeets Jan 29 2018