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Odd numbers of the form 4n+1 for which Jacobi-first-non-one(4n-1) differs from Jacobi-first-non-one(4n+1).
3

%I #17 Mar 31 2018 16:59:50

%S 49,73,121,169,193,289,313,361,409,433,481,529,553,649,673,721,769,

%T 793,841,889,913,961,1009,1033,1129,1153,1201,1249,1273,1321,1369,

%U 1393,1489,1513,1561,1609,1633,1681,1729,1753,1801,1849,1873,1969

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

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

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

%t 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 *)

%o (PARI) jfno(n) = my(k = 1); while(kronecker(k, n) == 1, k++); k;

%o lista(nn) = {forstep(n=5, nn, 4, if (jfno(n-2) != jfno(n), print1(n, ", ")););} \\ _Michel Marcus_, Jan 30 2018

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

%K nonn

%O 1,1

%A _Antti Karttunen_, Aug 27 2005