A122785 Nonprimes m such that 8^m == 8 (mod m).

1, 4, 8, 9, 14, 21, 28, 45, 56, 63, 65, 105, 117, 133, 153, 231, 273, 292, 341, 481, 511, 561, 585, 645, 651, 861, 949, 1001, 1016, 1105, 1106, 1281, 1288, 1365, 1387, 1417, 1541, 1649, 1661, 1729, 1736, 1785, 1905, 2044, 2047, 2169, 2465, 2501, 2696, 2701, 2821, 3145, 3171, 3201, 3277, 3605, 3641, 4005

Offset

1,2

Comments

Theorem: If both numbers q and 2q-1 are primes and m=q*(2q-1) then 8^m==8 (mod m) (m is in the sequence) iff q is of the form 4k+1. 2701,18721,49141,104653,226801,665281,721801,... are such terms.

Links

Table of n, a(n) for n=1..58.

Maple

q:= m-> not isprime(m) and 8&^m mod m = 8 mod m:
select(q, [$1..5000])[];  # Alois P. Heinz, Apr 19 2022

Mathematica

Select[Range[6000], ! PrimeQ[ # ] && Mod[8^#, # ] == Mod[8, # ] &]

Crossrefs

Cf. A020137, A001567.

Sequence in context: A085711 A182491 A281686 * A280450 A137055 A078177

Adjacent sequences: A122782 A122783 A122784 * A122786 A122787 A122788

Keyword

nonn

Author

Farideh Firoozbakht, Sep 12 2006

Extensions

Missing a(8)-a(18) inserted by Georg Fischer, Apr 19 2022

Status

approved