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A270697 Composite numbers n == 3 (mod 4) such that (1 + i)^n == 1 - i (mod n), where i = sqrt(-1). 4
2047, 42799, 90751, 256999, 271951, 476971, 514447, 741751, 877099, 916327, 1302451, 1325843, 1397419, 1441091, 1507963, 1530787, 1907851, 2004403, 2205967, 2304167, 2748023, 2811271, 2953711, 2976487, 3090091, 3116107, 4469471, 4863127, 5016191 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Composite n == 3 (mod 4) such that 2*(-4)^((n-3)/4) == -1 (mod n). - Robert Israel, Mar 21 2016

2*(-4)^((p-3)/4) == -1 (mod p) is satisfied by all primes p == 3 (mod 4), see A318908. - Jianing Song, Sep 05 2018

Numbers in A047713 that are congruent to 3 mod 4. Most terms are congruent to 7 mod 8. For terms congruent to 3 mod 8, see A244628. - Jianing Song, Sep 05 2018

LINKS

Jianing Song, Table of n, a(n) for n = 1..111 (using data from A047713)

MAPLE

select(t -> not isprime(t) and 1 + 2*(-4) &^ ((t-3)/4) mod t = 0, [seq(i, i=7..10^7, 4)]); # Robert Israel, Mar 21 2016

MATHEMATICA

Select[3 + 4*Range[10000000], PrimeQ[#] == False && PowerMod[1 + I, #, #] == Mod[1 - I, #] &]

PROG

(PARI) forstep(n=3, 10^7, 4, if(Mod(2, n)^((n-1)/2)==kronecker(2, n) && !isprime(n), print1(n, ", ")))

CROSSREFS

Subsequence of A001567 and A047713.

A244628 is a proper subsequence.

Cf. A270698, A318908.

Sequence in context: A141232 A062568 A180065 * A075954 A011561 A160960

Adjacent sequences:  A270694 A270695 A270696 * A270698 A270699 A270700

KEYWORD

nonn

AUTHOR

José María Grau Ribas, Mar 21 2016

STATUS

approved

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Last modified October 22 20:57 EDT 2018. Contains 316502 sequences. (Running on oeis4.)