cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A375247 Fluctuations of the number of biquadrate integers not exceeding 10^n.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, -1, 3, 0, 8, 4, -5, 10, 1, -11, -13, -40, -19, -99, 33, -63, 91, 88, 148, -4, -805, 185, 613, -159, -3530, -2419, -5593, -4263, 6633, -553, -3187, -5923, -40742
Offset: 0

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Author

Chai Wah Wu, Aug 08 2024

Keywords

Comments

The asymptotic density of biquadrate integers is 90/Pi^4 = 1/zeta(4) = 0.92393840292159... The number of biquadrate integers not exceeding N is approximately N/zeta(4). a(n) gives the difference between this number (A375246) and the linear estimate N/zeta(4) rounded to the nearest integer when N is a power of 10.

Crossrefs

Cf. A060431, A013662, A046100, A215267, A307430, A375245, A375246.

Formula

a(n) = A375246(10^n)-round(10^n/zeta(4)).
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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