A216021 a(n) = modlg(n^n, 2^n), where modlg is the function defined in A215894: modlg(a,b) = floor(a / b^floor(logb(a))), logb is the logarithm base b.

1, 1, 3, 1, 3, 11, 50, 1, 2, 9, 33, 129, 550, 2526, 12445, 1, 2, 8, 26, 86, 302, 1103, 4216, 16834, 70064, 303520, 1366413, 6383595, 30907397, 154895272, 802588710, 1, 2, 7, 23, 69, 215, 685, 2242, 7523, 25881, 91237, 329377, 1217078, 4600595, 17781207, 70234475

Offset

1,3

Comments

a(2^k) = 1.

In base B representation of A, modlg(A,B) is the most significant digit:

A = C0 + C1*B + C2*B^2 + ... + Cn*B^n, Cn = modlg(A,B), C0 = A mod B.

Links

Table of n, a(n) for n=1..47.

Example

a(5) = modlg(5^5, 2^5) = floor(3125 / 32^floor(log32(3125))) = floor(3125/32^2) = 3.
a(7) = modlg(7^7, 2^7) = floor(823543 / 128^floor(log128(823543))) = floor(823543/128^2) = 50.

Prog

(Python)
import math
def modiv(a, b):
    return a - b*int(a/b)
def modlg(a, b):
    return a // b**int(math.log(a, b))
for n in range(1, 77):
    print modlg(n**n, 2**n),

Crossrefs

Cf. A215894.

Sequence in context: A204134 A233168 A001351 * A327149 A351372 A356411

Adjacent sequences: A216018 A216019 A216020 * A216022 A216023 A216024

Keyword

nonn

Author

Alex Ratushnyak, Aug 29 2012

Status

approved