A160509 Decimal expansion of 1/log(phi).

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

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.18.2, p. 159.

D. E. Knuth, The Art of Computer Programming, Vol 1: Fundamental Algorithms, Addison-Wesley, 1968, Appendix B, Table 1.

Links

Table of n, a(n) for n=1..105.

J. D. Cloud, Problem E 1636, The American Mathematical Monthly, Vol. 70, No. 9 (1963), p. 1005; Number of Fibonacci Numbers Not Exceeding N, Solution to Problem E 1636 by William D. Jackson, ibid., Vol. 71, No. 7 (1964), p. 798.

H. W. Gould, Non-Fibonacci Numbers, The Fibonacci Quarterly, Vol. 3, No. 3 (1965), pp. 177-183.

Douglas Lind, Problem H-74, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 3, No. 4 (1965), p. 300; A Better Problem Solution, Solution to Problem H-74, ibid., Vol. 4, No. 1 (1966), pp. 58-59.

Index entries for transcendental numbers.

Formula

From Amiram Eldar, Feb 05 2022: (Start)

Equals 1/A002390.

Equals lim_{n->oo} A072649(n)/log(n) (Cloud, 1963). (End)

Example

2.07808692123502753760132260611779576774219226778328...

Mathematica

RealDigits[1/Log@GoldenRatio, 10, 111][[1]] (* Robert G. Wilson v, May 29 2009 *)

Prog

(PARI) 1/asinh(1/2) \\ Charles R Greathouse IV, Jan 04 2016

Crossrefs

Cf. A001622, A002390, A072649.

Sequence in context: A380794 A352615 A377557 * A243444 A256293 A272002

Adjacent sequences: A160506 A160507 A160508 * A160510 A160511 A160512

Keyword

cons,nonn

Author

Hagen von Eitzen, May 16 2009

Extensions

More terms from Robert G. Wilson v, May 29 2009

Status

approved