A016630 Decimal expansion of log(7).

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

Offset

1,2

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.

Uhler, Horace S.; Recalculation and extension of the modulus and of the logarithms of 2, 3, 5, 7 and 17. Proc. Nat. Acad. Sci. U. S. A. 26, (1940). 205-212.

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

Formula

From Peter Bala, Nov 11 2019: (Start)

log(7) = 2*sqrt(3)*Integral_{t = 0..sqrt(3)/3} (1 - t^4)/(1 + t^6) dt.

log(7) = (8/9)*Sum_{n >= 0} (12*n+11)/((6*n+1)*(6*n+5))*(-1/27)^n.

log(7) = 6*Sum_{n >= 0} ( 243/(12*n+1) - 27/(12*n+5) - 9/(12*n+7) + 1/(12*n+11) )*(1/729)^(n+1), a BPP-type formula. (End)

log(7) = 2*Sum_{n >= 1} 1/(n*P(n, 4/3)*P(n-1, 4/3)), where P(n, x) denotes the n-th Legendre polynomial. The first 20 terms of the series gives the approximation log(7) = 1.945910149055(27...), correct to 12 decimal places. - Peter Bala, Mar 18 2024

Example

1.945910149055313305105352743443179729637084729581861188459390149937579...

Mathematica

First[RealDigits[Log[7], 10, 100]] (* Paolo Xausa, Mar 21 2024 *)

Prog

(PARI) default(realprecision, 20080); x=log(7); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016630.txt", n, " ", d)); \\ Harry J. Smith, May 16 2009

Crossrefs

Cf. A016735 Continued fraction.

Sequence in context: A154900 A246546 A172197 * A213614 A099281 A086240

Adjacent sequences: A016627 A016628 A016629 * A016631 A016632 A016633

Keyword

nonn,cons

Author

N. J. A. Sloane

Status

approved