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A122780
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Nonprimes k such that 3^k == 3 (mod k).
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16
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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66 is composite and 3^66 = 66*468229611858069884271524875811 + 3 so 66 is in the sequence.
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MAPLE
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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;
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MATHEMATICA
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Select[Range[30000], ! PrimeQ[ # ] && Mod[3^#, # ] == Mod[3, # ] &]
Join[{1}, Select[Range[20000], !PrimeQ[#]&&PowerMod[3, #, #]==3&]] (* Harvey P. Dale, Apr 30 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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