A356638 Odd composite numbers k such that 2^((k-1)/2) == -1 (mod k).

3277, 29341, 49141, 80581, 88357, 104653, 196093, 314821, 458989, 476971, 489997, 800605, 838861, 873181, 877099, 1004653, 1251949, 1302451, 1325843, 1373653, 1397419, 1441091, 1507963, 1509709, 1530787, 1678541, 1811573, 1907851, 1987021, 2004403, 2269093

Offset

1,1

Comments

Counterexamples (pseudoprimes) to the hypothesis that this congruence is sufficient to prove that an odd number is prime.

Compare with Proth's theorem.

Links

Table of n, a(n) for n=1..31.

Mathematica

Select[Range[1, 2.5*10^6, 2], CompositeQ[#] && PowerMod[2, (# - 1)/2, #] == # - 1 &] (* Amiram Eldar, Aug 19 2022 *)

Prog

(PARI) forstep(k=3, 10^8, 2, isprime(k)&&next(); Mod(2, k)^((k-1)/2)==-1&&print1(k, ", "))

Crossrefs

Cf. A244626, A244628.

Sequence in context: A141629 A116460 A245482 * A244626 A270204 A293626

Adjacent sequences: A356635 A356636 A356637 * A356639 A356640 A356641

Keyword

nonn

Author

Jeppe Stig Nielsen, Aug 19 2022

Status

approved