A373745 Maximum length of a run of alternating bits in the base-2 representation of prime(n).

2, 1, 3, 1, 3, 3, 2, 2, 3, 3, 1, 4, 4, 5, 3, 5, 3, 3, 2, 2, 3, 2, 4, 3, 2, 4, 2, 5, 3, 2, 1, 2, 3, 4, 6, 4, 3, 4, 4, 5, 3, 5, 3, 2, 4, 2, 4, 3, 2, 4, 4, 3, 2, 3, 2, 2, 3, 2, 6, 2, 3, 4, 2, 3, 2, 3, 4, 6, 5, 5, 3, 3, 3, 5, 3, 3, 4, 3, 3, 2, 4, 4, 5, 3, 3, 3, 2, 3, 3, 2, 4, 3, 2, 5

Offset

1,1

Links

Table of n, a(n) for n=1..94.

Formula

a(n) = A374176(A000040(n)) + 1. - Alois P. Heinz, Jul 10 2024

Example

149 = prime(35) = 10010101_2 has two alternating bit runs of lengths 2 and 6: 10_010101, and thus a(35) = 6.

Maple

b:= n-> `if`(n<2, [n$2], (f-> (t-> [t, max(t, f[2])])(
        `if`(n mod 4 in {0, 3}, 1, f[1]+1)))(b(iquo(n, 2)))):
a:= n-> b(ithprime(n))[2]:
seq(a(n), n=1..94);  # Alois P. Heinz, Jul 08 2024

Prog

(Python)
from sympy import prime
def A373745(n):
    s = bin(prime(n))[2:]
    return next(i for i in range(len(s), 0, -1) if ('01'*(i+1>>1))[:i] in s or ('10'*(i+1>>1))[:i] in s) # Chai Wah Wu, Jul 10 2024

Crossrefs

Cf. A000040, A374176.

Sequence in context: A244797 A308659 A145652 * A368290 A111248 A100714

Adjacent sequences: A373742 A373743 A373744 * A373746 A373747 A373748

Keyword

nonn,base,easy

Author

James S. DeArmon, Jun 16 2024

Status

approved