A112057 Odd numbers of the form 4n+1 for which Jacobi-first-non-one(4n-1) differs from Jacobi-first-non-one(4n+1).

49, 73, 121, 169, 193, 289, 313, 361, 409, 433, 481, 529, 553, 649, 673, 721, 769, 793, 841, 889, 913, 961, 1009, 1033, 1129, 1153, 1201, 1249, 1273, 1321, 1369, 1393, 1489, 1513, 1561, 1609, 1633, 1681, 1729, 1753, 1801, 1849, 1873, 1969

Offset: 1

Author

Antti Karttunen, Aug 27 2005

Keywords

• nonn

Comments

The definition of Jacobi-first-non-one is given in A112056.

Crossrefs

a(n) = A112056(n)+2 = A112058(n)+1.

Programs

Mathematica

a112046[n_]:=Block[{i=1}, While[JacobiSymbol[i, 2n + 1]==1, i++]; i]; 4*Select[Range[1000], a112046[2#] - a112046[2# - 1] != 0 &] + 1 (* Indranil Ghosh, May 25 2017 *)

PARI

jfno(n) = my(k = 1); while(kronecker(k, n) == 1, k++); k;
lista(nn) = {forstep(n=5, nn, 4, if (jfno(n-2) != jfno(n), print1(n, ", ")););} \\ Michel Marcus, Jan 30 2018

Formula

a(n) = 4*A112054(n) + 1.