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A015950 Numbers n such that n | 4^n + 1. 5
1, 5, 25, 125, 205, 625, 1025, 2525, 3125, 5125, 8405, 12625, 15625, 25625, 42025, 63125, 78125, 103525, 128125, 168305, 202525, 210125, 255025, 315625, 344605, 390625, 517625, 640625, 841525, 875125, 1012625, 1050625, 1275125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From Robert Israel, Sep 14 2017: (Start)

All terms except 1 are congruent to 5 mod 20.

If n is a term and prime p | n, then n*p is a term.

All prime factors of terms == 1 (mod 4).

If p is a prime == 1 (mod 4) and the order of 4 (mod p) is 2m where m is in the sequence, then m*p is in the sequence. (End)

LINKS

Robert Israel, Table of n, a(n) for n = 1..325

EXAMPLE

4^5 + 1 = 1025 and 1025 is divisible by 5, so 5 is a term.

MAPLE

select(n -> 4 &^ n + 1 mod n = 0, [1, seq(i, i=5..10^7, 20)]); # Robert Israel, Sep 14 2017

PROG

(PARI) isok(n) = Mod(4, n)^n == -1; \\ Michel Marcus, Sep 15 2017

CROSSREFS

Cf. A015945.

Sequence in context: A271380 A036149 A061974 * A267780 A228736 A126642

Adjacent sequences:  A015947 A015948 A015949 * A015951 A015952 A015953

KEYWORD

nonn,changed

AUTHOR

Robert G. Wilson v

STATUS

approved

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Last modified September 21 15:13 EDT 2017. Contains 292300 sequences.