A112056 - OEIS

%I #11 May 07 2021 00:46:32

%S 47,71,119,167,191,287,311,359,407,431,479,527,551,647,671,719,767,

%T 791,839,887,911,959,1007,1031,1127,1151,1199,1247,1271,1319,1367,

%U 1391,1487,1511,1559,1607,1631,1679,1727,1751,1799,1847,1871,1967

%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 Here Jacobi-first-non-one(m) (for odd numbers m) is defined as the first value of i >= 1, for which Jacobi symbol J(i,m) is not +1 (i.e. is either 0 or -1).

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

%F a(n) = A112057(n)-2 = A112058(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 24 2017 *)

%o (Python)

%o from sympy import jacobi_symbol as J

%o def a112046(n):

%o     i=1

%o     while True:

%o         if J(i, 2*n + 1)!=1: return i

%o         else: i+=1

%o def a(n): return a112046(2*n) - a112046(2*n - 1)

%o print([4*n - 1 for n in range(1, 1001) if a(n)!=0]) # _Indranil Ghosh_, May 24 2017

%Y Cf. A112054, A112057, A112058.

%K nonn

%O 1,1

%A _Antti Karttunen_, Aug 27 2005