A122782 Nonprimes n such that 5^n==5 (mod n).

1, 4, 10, 15, 20, 65, 124, 190, 217, 310, 435, 561, 781, 1105, 1541, 1729, 1891, 2465, 2821, 3565, 3820, 4123, 4495, 5461, 5611, 5662, 5731, 6601, 6735, 7449, 7813, 8029, 8290, 8911, 9881, 10585, 11041, 11476, 12801, 13021, 13333, 13981, 14981

Offset: 1

Author

Farideh Firoozbakht, Sep 12 2006

Keywords

• nonn

Comments

Theorem: If both numbers q and 2q-1 are primes then n=q*(2q-1) is in the sequence iff q=3 or q is of the form 10k+1. 15,1891,88831,146611,218791,721801,873181,... are such terms.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005936.

Programs

Mathematica

Select[Range[15000], ! PrimeQ[ # ] && Mod[5^#, # ] == Mod[5, # ] &]
Join[{1,4},Select[Range[15000],CompositeQ[#]&&PowerMod[5,#,#]==5&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 13 2021 *)