A270698 Composite numbers k == 1 (mod 4) such that (1 + i)^k == 1 + i (mod k), where i = sqrt(-1).

561, 1105, 1729, 1905, 2465, 3277, 4033, 4681, 6601, 8321, 8481, 10585, 12801, 15841, 16705, 18705, 25761, 29341, 30121, 33153, 34945, 41041, 46657, 49141, 52633, 62745, 65281, 74665, 75361, 80581, 85489, 87249, 88357, 104653, 113201, 115921, 126217, 129921

Offset: 1

Author

José María Grau Ribas, Mar 21 2016

Keywords

• nonn

Comments

From Jianing Song, Sep 05 2018: (Start)

Numbers in A047713 that are congruent to 1 mod 4. Most terms are congruent to 1 mod 8. For terms congruent to 5 mod 8, see A244626.

Also composite k == 1 (mod 4) such that (-4)^((k-1)/4) == 1 (mod k). Note that this is satisfied by all primes == 1 (mod 4), see A318898. (End)

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..889 from Jianing Song using data from A047713)

Crossrefs

Subsequence of A001567 and A047713.

A244626 is a proper subsequence.

Cf. A006971, A270697, A318898.

Programs

Mathematica

Select[1 + 4*Range[100000], PrimeQ[#] == False && PowerMod[1 + I, #, #] == 1 + I &]

PARI

forstep(n=5, 10^5, 4, if(Mod(2, n)^((n-1)/2)==kronecker(2, n) && !isprime(n), print1(n, ", "))) \\ Jianing Song, Sep 06 2018