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Signature sequence of Soldner's constant (A070769).
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%I #26 May 27 2024 11:47:11

%S 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,

%T 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,

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

%N Signature sequence of Soldner's constant (A070769).

%C 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.

%C The plot looks surprisingly regular. - _T. D. Noe_, Jul 23 2013

%C Where does this first differ from A133334? - _R. J. Mathar_, Jul 30 2013

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SoldnersConstant.html">Soldner's Constant</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LogarithmicIntegral.html">Logarithmic Integral</a>.

%H <a href="/index/Si#signature_sequences">Index entries for sequences related to signature sequences</a>

%t 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 *)

%Y Cf. A070769, A099803.

%K nonn

%O 1,2

%A _Casey Mongoven_, Jul 16 2013