A352886 - OEIS

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

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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