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A163366 a(n) = (-1)^floor((prime(n)+2)/2) mod prime(n). 3
1, 1, 4, 1, 1, 12, 16, 1, 1, 28, 1, 36, 40, 1, 1, 52, 1, 60, 1, 1, 72, 1, 1, 88, 96, 100, 1, 1, 108, 112, 1, 1, 136, 1, 148, 1, 156, 1, 1, 172, 1, 180, 1, 192, 196, 1, 1, 1, 1, 228, 232, 1, 240, 1, 256, 1, 268, 1, 276, 280, 1, 292, 1, 1, 312, 316, 1, 336, 1, 348, 352, 1, 1, 372, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Remove the '1's from the sequence to get A152680.

Product modulo p of the quadratic residues of p, where p = prime(n). [Jonathan Sondow, May 14 2010]

REFERENCES

Carl-Erik Froeberg, On sums and products of quadratic residues, BIT, Nord. Tidskr. Inf.-behandl. 11 (1971) 389-398. [Jonathan Sondow, May 14 2010]

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Rahul Gupta, Algorithmic Number Theory, Section 24.5 [Jonathan Sondow, May 14 2010]

FORMULA

a(n)*A177863(n) == -1 (mod prime(n)), by Wilson's theorem. - Jonathan Sondow, May 14 2010

a(n) = A177860(n) modulo prime(n). - Jonathan Sondow, May 14 2010

EXAMPLE

a(4) = 1 because the quadratic residues of prime(4) = 7 are 1, 2, and 4, and 1*2*4 = 8 == 1 (mod 7). - Jonathan Sondow, May 14 2010

MAPLE

seq((-1)^iquo(ithprime(i)+2, 2) mod ithprime(i), i=1..113);

MATHEMATICA

Table[Mod[ Apply[Times, Flatten[Position[ Table[JacobiSymbol[i, Prime[n]], {i, 1, Prime[n] - 1}], 1]]], Prime[n]], {n, 1, 80}] (* Jonathan Sondow, May 14 2010 *)

CROSSREFS

Cf. A152680, A005098, A002144, A009003.

Cf. A177860, A177863. - Jonathan Sondow, May 14 2010

Sequence in context: A220688 A146990 A051433 * A181145 A227203 A140070

Adjacent sequences:  A163363 A163364 A163365 * A163367 A163368 A163369

KEYWORD

nonn

AUTHOR

Peter Luschny, Jul 25 2009

STATUS

approved

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Last modified August 6 17:06 EDT 2020. Contains 336255 sequences. (Running on oeis4.)