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

Author

Felix Fröhlich, Apr 07 2022

Keywords

• nonn
• easy
• base

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).

Examples

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

Links

• 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.

Crossrefs

Cf. A008683, A027375, A242138, A242139.

Programs

PARI

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

Formula

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