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Decimal expansion of 1/log(phi).
1

%I #28 Jan 05 2025 19:51:39

%S 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,

%T 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,

%U 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

%N Decimal expansion of 1/log(phi).

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

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

%H J. D. Cloud, <a href="https://www.jstor.org/stable/2313072">Problem E 1636</a>, The American Mathematical Monthly, Vol. 70, No. 9 (1963), p. 1005; <a href="https://doi.org/10.2307/2310916">Number of Fibonacci Numbers Not Exceeding N</a>, Solution to Problem E 1636 by William D. Jackson, ibid., Vol. 71, No. 7 (1964), p. 798.

%H H. W. Gould, <a href="https://fq.math.ca/Scanned/3-3/gould.pdf">Non-Fibonacci Numbers</a>, The Fibonacci Quarterly, Vol. 3, No. 3 (1965), pp. 177-183.

%H Douglas Lind, <a href="https://fq.math.ca/Scanned/3-4/advanced3-4.pdf">Problem H-74</a>, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 3, No. 4 (1965), p. 300; <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/4-1/advanced4-1.pdf">A Better Problem Solution</a>, Solution to Problem H-74, ibid., Vol. 4, No. 1 (1966), pp. 58-59.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F From _Amiram Eldar_, Feb 05 2022: (Start)

%F Equals 1/A002390.

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

%e 2.07808692123502753760132260611779576774219226778328...

%t RealDigits[1/Log@GoldenRatio, 10, 111][[1]] (* _Robert G. Wilson v_, May 29 2009 *)

%o (PARI) 1/asinh(1/2) \\ _Charles R Greathouse IV_, Jan 04 2016

%Y Cf. A001622, A002390, A072649.

%K cons,nonn

%O 1,1

%A _Hagen von Eitzen_, May 16 2009

%E More terms from _Robert G. Wilson v_, May 29 2009