

A182490


Number of Carmichael numbers between 2^n and 2^(n+1).


4



0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 3, 1, 5, 4, 4, 10, 12, 10, 14, 26, 35, 32, 52, 76, 85, 108, 173, 208, 254, 328, 428, 563, 693, 928, 1130, 1454, 1879, 2481, 3234, 4164, 5231, 6890, 8855, 11309, 14905, 19227, 25040, 32035, 41615, 53710, 70061, 91228, 118940, 154659, 201004, 263363, 343053, 447613, 586096, 765319, 1000803, 1311065, 1716615, 2253877, 2956272, 3879379
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OFFSET

1,10


COMMENTS

While there may be an infinite number of Carmichael numbers, the ratio of Carmichael composites to odd composites (A094812), when looked at as a function of the poweroftwo interval, apparently approaches 0 as the interval number n increases. It is 0.00533333 for n=10 but decreases to 0.00009035 by n=18 and is 0.00000254 at n=26, and looks like it could be reasonably modeled by 1/(A + B*log(n) + C*(log(n))^2 + D*(log(n)^3)).


LINKS



PROG

(Magma)
for i:= 1 to 25 do
icount:=0;
for k := 2^i +1 to 2^(i+1)1 by 2 do
if (not IsPrime(k) and (k mod CarmichaelLambda(k) eq 1)) then icount +:=1;
end if;
end for;
i, icount;
end for;


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

Extended to a(68) with data from R. Pinch by Brad Clardy, May 18 2014


STATUS

approved



