A016687 Decimal expansion of log(64) = 6*log(2).

4, 1, 5, 8, 8, 8, 3, 0, 8, 3, 3, 5, 9, 6, 7, 1, 8, 5, 6, 5, 0, 3, 3, 9, 2, 7, 2, 8, 7, 4, 9, 0, 5, 9, 4, 0, 8, 4, 5, 3, 0, 0, 0, 8, 0, 6, 1, 6, 1, 5, 3, 1, 5, 2, 4, 7, 2, 4, 0, 8, 0, 0, 5, 6, 9, 6, 0, 3, 6, 1, 7, 3, 1, 8, 1, 8, 1, 6, 8, 2, 9, 3, 6, 3, 5, 1, 7, 9, 9, 6, 1, 9, 7, 8, 5, 1, 2, 1, 2

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Examples

			4.158883083359671856503392728749059408453000806161531524724080056960361...
		

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 2.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• Index entries for transcendental numbers

Crossrefs

Cf. A002162, A005900, A016492 (continued fraction), A016627, A016631.

Programs

Mathematica

RealDigits[Log[64],10,120][[1]] (* Harvey P. Dale, May 06 2022 *)

PARI

default(realprecision, 20080); x=log(64); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016687.txt", n, " ", d)); \\ Harry J. Smith, May 22 2009

Formula

Equals 2*A016631 = 3*A016627 = 6*A002162. - Alois P. Heinz, Aug 07 2023

From Peter Bala, Mar 05 2024: (Start)

log(64) = 4 + Sum_{n >= 1} (-1)^(n+1)/(p(n)*p(n+1)), where p(n) = n*(2*n^2 + 1)/3 = A005900.

Continued fraction: log(64) = 4 + 1/(6 + (1*2)/(6 + (2*3)/(6 + (3*4)/(6 + (4*5)/(6 + ... ))))). See A142983. Cf. A016627. (End)