A099803 -id:A099803 - cp's OEIS frontend

A160923 Continued fraction for 1/6 + Soldner's constant.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 11, 1, 3, 1, 1, 4, 1, 1, 1, 6, 2, 8, 3, 4, 20, 1, 7, 2, 1, 2, 3, 2, 1, 6, 1, 18, 1, 3, 1, 1, 4, 1, 2, 2, 1

Offset: 1

Fredrik Johansson, May 30 2009

1/6 + Soldner's constant differs from the golden ratio by less than 2*10^-6. (1/6 + Soldner's constant = 1.61803590...; golden ratio = 1.61803398...). Hence the long initial sequence of 1's.

Soldner's constant is A099803 Golden ratio is A000012

ContinuedFraction[1/6 + FindRoot[LogIntegral[x], {x, 1.5}, WorkingPrecision->1000][[1,2]], 50]

A227539 Signature sequence of Soldner's constant (A070769).

Original entry on oeis.org

1, 2, 1, 3, 2, 1, 4, 3, 2, 5, 1, 4, 3, 6, 2, 5, 1, 4, 7, 3, 6, 2, 5, 8, 1, 4, 7, 3, 6, 9, 2, 5, 8, 1, 4, 7, 10, 3, 6, 9, 2, 5, 8, 11, 1, 4, 7, 10, 3, 6, 9, 12, 2, 5, 8, 11, 1, 4, 7, 10, 13, 3, 6, 9, 12, 2, 5, 8, 11, 14, 1, 4, 7, 10, 13, 3, 6, 9, 12, 15, 2, 5, 8

Offset: 1

Casey Mongoven, Jul 16 2013

nonn

Arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x; the sequence of j's is the signature of 1/x.
The plot looks surprisingly regular. - T. D. Noe, Jul 23 2013
Where does this first differ from A133334? - R. J. Mathar, Jul 30 2013

Clark Kimberling, Fractal Sequences and Interspersions, Ars Combinatoria 45 (1997) 157-168.

Eric Weisstein's World of Mathematics, Soldner's Constant.
Eric Weisstein's World of Mathematics, Logarithmic Integral.
Index entries for sequences related to signature sequences

Cf. A070769, A099803.

x = FindRoot[LogIntegral[x] == 0, {x, 2}, WorkingPrecision -> 105][[1,2]]; Take[Transpose[Sort[Flatten[Table[{i + j*x, i}, {i, 30}, {j, 20}], 1], #1[[1]] < #2[[1]] &]][[2]], 100] (* T. D. Noe, Jul 23 2013 *)

cp's OEIS Frontend

A160923 Continued fraction for 1/6 + Soldner's constant.

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