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A122780 Nonprimes k such that 3^k == 3 (mod k). 16
1, 6, 66, 91, 121, 286, 561, 671, 703, 726, 949, 1105, 1541, 1729, 1891, 2465, 2665, 2701, 2821, 3281, 3367, 3751, 4961, 5551, 6601, 7107, 7381, 8205, 8401, 8646, 8911, 10585, 11011, 12403, 14383, 15203, 15457, 15841, 16471, 16531, 18721, 19345 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Theorem: If q!=3 and both numbers q and (2q-1) are primes then k=q*(2q-1) is in the sequence. 6, 91, 703, 1891, 2701, 12403, 18721, 38503, 49141, ... is the related subsequence.
The terms > 1 and coprime to 3 of this sequence are the base-3 pseudoprimes, A005935. - M. F. Hasler, Jul 19 2012 [Corrected by Jianing Song, Feb 06 2019]
LINKS
EXAMPLE
66 is composite and 3^66 = 66*468229611858069884271524875811 + 3 so 66 is in the sequence.
MAPLE
isA122780 := proc(n)
if isprime(n) then
false;
else
modp( 3 &^ n, n) = modp(3, n) ;
end if;
end proc:
for n from 1 do
if isA122780(n) then
print(n) ;
end if;
end do: # R. J. Mathar, Jul 15 2012
MATHEMATICA
Select[Range[30000], ! PrimeQ[ # ] && Mod[3^#, # ] == Mod[3, # ] &]
Join[{1}, Select[Range[20000], !PrimeQ[#]&&PowerMod[3, #, #]==3&]] (* Harvey P. Dale, Apr 30 2023 *)
PROG
(PARI) is_A122780(n)={n>0 & Mod(3, n)^n==3 & !ispseudoprime(n)} \\ M. F. Hasler, Jul 19 2012
CROSSREFS
Sequence in context: A137121 A110222 A119230 * A153514 A119144 A153087
KEYWORD
easy,nonn
AUTHOR
Farideh Firoozbakht, Sep 11 2006
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)