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A112054 Indices where A112053 is not zero. 7
12, 18, 30, 42, 48, 72, 78, 90, 102, 108, 120, 132, 138, 162, 168, 180, 192, 198, 210, 222, 228, 240, 252, 258, 282, 288, 300, 312, 318, 330, 342, 348, 372, 378, 390, 402, 408, 420, 432, 438, 450, 462, 468, 492, 498, 510, 522, 528, 540, 552, 558, 582, 588 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These are all divisible by 6, as J(2,m) = +1 if m = 1 or 7 mod 8 and -1 if m = 3 or 5 mod 8 and J(3,m) = +1 if m = 1 or 11 mod 12, -1 if m = 5 or 7 mod 12 and 0 if m = 3 or 9 mod 12 (where Jacobi symbol J(i,m) returns +1 if i is quadratic residue modulo odd number m), it follows that only when i=24*n it holds that J(2,i-1)=J(2,i+1)=J(3,i-1)=J(3,i+1)=+1 and thus only then the function A112046 (and A112053) depends on values of J(k>3,m).

LINKS

Table of n, a(n) for n=1..53.

MATHEMATICA

a112046[n_]:=Block[{i=1}, While[JacobiSymbol[i, 2n + 1]==1, i++]; i]; Select[Range[1000], a112046[2#] - a112046[2# - 1] != 0 &] (* Indranil Ghosh, May 24 2017 *)

PROG

(Python)

from sympy import jacobi_symbol as J

def a112046(n):

    i=1

    while True:

        if J(i, 2*n + 1)!=1: return i

        else: i+=1

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

print [n for n in xrange(1, 1001) if a(n)!=0] # Indranil Ghosh, May 24 2017

CROSSREFS

Cf. A112058(n) = 4*a(n). A112055(n) = a(n)/6.

Sequence in context: A006622 A124269 A179192 * A225576 A275082 A256753

Adjacent sequences:  A112051 A112052 A112053 * A112055 A112056 A112057

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 27 2005

STATUS

approved

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Last modified March 19 00:03 EDT 2019. Contains 321305 sequences. (Running on oeis4.)