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A180943
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Odd composite numbers m for which 12*|A000367((m+1)/2)|==(-1)^{(m-1)/ 2}* A002445((m+1)/2) (mod m).
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1
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33, 169, 481, 561, 793, 805, 949, 1105, 1261, 1417, 1645, 1729, 2041, 2353, 2465, 2509, 2821, 2977, 3133, 3421, 3445, 3601, 4069, 4123, 4381, 4537, 4849, 5161, 5317, 5473, 5629, 5941, 6061, 6205, 6601, 7033, 7093, 7189, 7501, 7813, 7885, 7969, 8113
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OFFSET
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1,1
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COMMENTS
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These are pseudoprimes in the sense that the congruence of the definition is valid if any odd prime is substituted for m.
Entries of the form m = 4*k+3 are apparently rare: 4123, 8911, ...
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LINKS
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MAPLE
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A000367 := proc(n) numer(bernoulli(2*n)) ; end proc:
A002445 := proc(n) denom(bernoulli(2*n)) ; end proc:
isA180943 := proc(m) if type(m, 'odd') and not isprime(m) then 12*abs(A000367((m+1)/2)) mod m = (-1)^((m-1)/2)*A002445((m+1)/2) mod m ; else false; end if; end proc:
A180943 := proc(n) option remember; if n = 1 then 33; else for a from procname(n-1)+2 by 2 do if isA180943(a) then return a; end if; end do: end if; end proc: # R. J. Mathar, Oct 24 2010
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MATHEMATICA
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nb[n_] := Numerator[BernoulliB[2n]];
db[n_] := Denominator[BernoulliB[2n]];
okQ[m_] := CompositeQ[m] && Mod[12*Abs[nb[(m+1)/2]], m] == Mod[(-1)^((m-1)/2)*db[(m+1)/2], m];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Comments rephrased and program added by R. J. Mathar, Oct 24 2010
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STATUS
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approved
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