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

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

0,10

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.

Links

Table of n, a(n) for n=0..39.

Formula

a(n) = A375246(10^n)-round(10^n/zeta(4)).

Crossrefs

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

Sequence in context: A144807 A157957 A201577 * A223854 A333567 A248424

Adjacent sequences: A375244 A375245 A375246 * A375248 A375249 A375250

Keyword

sign,more

Author

Chai Wah Wu, Aug 08 2024

Status

approved