A351964 The 2-adic valuation of A109812(n); The exponent of the highest power of 2 dividing A109812(n).

0, 1, 2, 0, 3, 0, 1, 4, 1, 0, 1, 2, 0, 1, 5, 0, 3, 0, 2, 0, 2, 0, 3, 0, 1, 0, 4, 0, 6, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 5, 0, 2, 0, 2, 0, 2, 4, 0, 3, 7, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 2, 1, 0, 1, 3, 0, 3, 0, 2, 0, 2, 6, 0, 5, 0, 4, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 4, 0, 1, 2, 0, 8, 0, 4

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for sequences related to binary expansion of n

Formula

a(n) = A007814(A109812(n)).

Prog

(PARI)
v109812 = readvec("b109812_to10e5.txt"); \\ Prepared from b-file data with gawk ' { print $2 } '
up_to = #v109812;
A109812(n) = v109812[n];
A007814(n) = valuation(n, 2);
A351964(n) = A007814(A109812(n));
(Python)
from itertools import count, islice
def A351964_gen(): # generator of terms
    yield 0
    l1, s, b = 1, 2, set()
    while True:
        for i in count(s):
            if not (i in b or i & l1):
                yield (~i&i-1).bit_length()
                l1 = i
                b.add(i)
                while s in b:
                    b.remove(s)
                    s += 1
                break
A351964_list = list(islice(A351964_gen(), 30)) # Chai Wah Wu, Jul 16 2022

Crossrefs

Cf. A007814, A109812, A351578, A351965.

Sequence in context: A133735 A238801 A095704 * A163496 A092241 A336124

Adjacent sequences: A351961 A351962 A351963 * A351965 A351966 A351967

Keyword

nonn,base

Author

Antti Karttunen, Apr 07 2022

Status

approved