A352886 Number of B-periodic numbers of bit pseudo-length n.

1, 0, 4, 0, 7, 3, 16, 0, 37, 0, 64, 18, 127, 0, 283, 0, 517, 66, 1024, 0, 2167, 15, 4096, 255, 8197, 0, 16906, 0, 32767, 1026, 65536, 78, 133087, 0, 262144, 4098, 524407, 0, 1056730, 0, 2097157, 16635, 4194304, 0, 8421247, 63, 16777711, 65538, 33554437, 0

Offset

4,3

Comments

For the definition of "B-periodic numbers" and "bit pseudo-length", see Dobeš, Kureš, 2010, p. 294. The first few terms are given in the table on p. 295.

The sequence counts periodic binary numbers of length n where the least-significant bit is 0 (see Dobeš, Kureš, 2010, p. 294).

Links

Table of n, a(n) for n=4..53.

J. Dobeš and M. Kureš, Search for Wieferich Primes through the use of Periodic Binary Strings, Serdica Journal of Computing, Vol. 4, No. 3 (2010), 293-300.

Formula

a(n) = (2^n - c(n) - 2)/2, where c(n) = Sum_{d|n} A008683(d)*2^(n/d).

Example

For n = 6: The B-periodic numbers of bit pseudo-length 6 are 101010, 100100, 010010 and 110110, so a(6) = 4.

Prog

(PARI) c(n) = sumdiv(n, d, moebius(d)*2^(n/d))
a(n) = (2^n - c(n) - 2)/2

Crossrefs

Cf. A008683, A027375, A242138, A242139.

Sequence in context: A251967 A330725 A057641 * A336029 A272876 A133930

Adjacent sequences: A352883 A352884 A352885 * A352887 A352888 A352889

Keyword

nonn,easy,base

Author

Felix Fröhlich, Apr 07 2022

Status

approved