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

Author

Farideh Firoozbakht, Sep 12 2006

Keywords

• nonn

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.

Crossrefs

Cf. A020137, A001567.

Programs

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, # ] &]

Extensions

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