The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A193031 Decimal expansion of the constant term of the reduction of 2^x by x^2->x+1. 2
 1, 3, 1, 9, 8, 7, 8, 7, 2, 4, 0, 2, 1, 1, 5, 6, 2, 7, 4, 4, 5, 9, 9, 7, 4, 2, 1, 2, 6, 3, 9, 3, 1, 3, 9, 3, 1, 8, 5, 9, 0, 4, 4, 6, 2, 3, 0, 5, 5, 5, 9, 7, 8, 8, 1, 5, 1, 7, 5, 9, 4, 3, 2, 8, 8, 5, 3, 2, 2, 7, 6, 2, 6, 1, 5, 1, 5, 6, 0, 3, 7, 5, 5, 3, 5, 6, 1, 2, 4, 8, 2, 3, 1, 1, 3, 2, 2, 0, 2, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010. LINKS FORMULA From Amiram Eldar, Jan 19 2022: (Start) Equals 1 + Sum_{k>=1} log(2)^k*Fibonacci(k-1)/k!. Equals (1 + (3+4^phi)/sqrt(5))/(phi*2^phi), where phi is the golden ratio (A001622). (End) EXAMPLE 1.3198787240211562744599742126393139318590... MATHEMATICA f[x_] := 2^x; r[n_] := Fibonacci[n]; c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n] u0 = N[Sum[c[n]*r[n - 1], {n, 0, 100}], 100] RealDigits[u0, 10] CROSSREFS Cf. A000045, A001622, A193010, A192232, A193032. Sequence in context: A114195 A185948 A016601 * A078416 A223533 A021973 Adjacent sequences:  A193028 A193029 A193030 * A193032 A193033 A193034 KEYWORD nonn,cons AUTHOR Clark Kimberling, Jul 14 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 25 09:37 EDT 2022. Contains 354066 sequences. (Running on oeis4.)