A094812 -id:A094812 - cp's OEIS frontend

A182490 Number of Carmichael numbers between 2^n and 2^(n+1).

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

Offset: 1

Brad Clardy, May 02 2012

nonn

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)).

Amiram Eldar, Table of n, a(n) for n = 1..72 (calculated using data from Claude Goutier)
Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
Richard Pinch, Carmichael numbers up to 10^21.

Cf. A002997.

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;

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

cp's OEIS Frontend

A182490 Number of Carmichael numbers between 2^n and 2^(n+1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Extensions