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

Author

Alex Ratushnyak, Aug 29 2012

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A215894.

Programs

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), end=', ')