A227197 -id:A227197 - cp's OEIS frontend

A227198 Odd terms in A227197.

9, 15, 25, 33, 39, 49, 57, 63, 81, 87, 95, 105, 111, 119, 121, 129, 135, 145, 153, 159, 169, 177, 183, 201, 207, 215, 225, 231, 249, 255, 265, 273, 279, 289, 297, 303, 321, 327, 335, 345, 351, 361, 369, 375, 385, 393, 399, 417, 423, 441, 447, 455, 465, 471, 489

Offset: 1

Antti Karttunen, Jul 06 2013

nonn

Gives all terms n for which A090368((n+1)/2) = A112046((n-1)/2).

Contains all odd squares. What else?

Cf. A227196, A227197, A090368, A112046.

A227196(n) = for(k=1, n, if(kronecker(k, n)<1, return(k)))
for(n=2,1000,if((0==kronecker(A227196(n),n)&&1==(n%2)),print1(n,", ")))

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.

Original entry on oeis.org

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

Antti Karttunen, Jul 06 2013

nonn

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

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

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

Cf. A227195, A227197, A227198, A112052.

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

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

cp's OEIS Frontend

A227198 Odd terms in A227197.

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