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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 (list; graph; refs; listen; history; text; internal format)
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 power-of-two 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
Amiram Eldar, Table of n, a(n) for n = 1..72 (calculated using data from Claude Goutier)
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
Cf. A002997.
Sequence in context: A044924 A057036 A069004 * A053274 A243926 A281013
KEYWORD
nonn
AUTHOR
Brad Clardy, May 02 2012
EXTENSIONS
Extended to a(50) by T. D. Noe, May 02 2012
Extended to a(68) with data from R. Pinch by Brad Clardy, May 18 2014
STATUS
approved

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Last modified May 22 15:18 EDT 2024. Contains 372758 sequences. (Running on oeis4.)