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

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

Author

Casey Mongoven, Jul 16 2013

Keywords

• nonn

Comments

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

References

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

Links

• 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

Crossrefs

Cf. A070769, A099803.

Programs

Mathematica

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 *)