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 A193032 Decimal expansion of the coefficient of x in the reduction of 2^x by x^2->x+1. 3
 1, 0, 8, 1, 3, 6, 5, 2, 8, 3, 9, 1, 6, 9, 6, 0, 7, 6, 7, 5, 5, 4, 8, 2, 1, 1, 0, 5, 4, 4, 8, 4, 4, 2, 6, 0, 2, 4, 9, 7, 0, 6, 5, 3, 8, 2, 2, 2, 3, 3, 6, 6, 4, 9, 1, 7, 8, 4, 8, 4, 4, 0, 9, 2, 0, 0, 2, 2, 4, 8, 5, 3, 2, 7, 2, 4, 6, 0, 6, 5, 9, 6, 9, 7, 2, 2, 3, 8, 2, 6, 1, 0, 1, 7, 4, 5, 4, 6, 7, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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 Sum_{k>=0} log(2)^k*Fibonacci(k)/k!. Equals (2^sqrt(5)-1)/(sqrt(5)*2^(phi-1)), where phi is the golden ratio (A001622). (End) EXAMPLE 1.081365283916960767554821105448442602497... MATHEMATICA f[x_] := 2^x; r[n_] := Fibonacci[n]; c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n] u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100] RealDigits[u1, 10] CROSSREFS Cf. A000045, A001622, A193010, A192232, A193031. Sequence in context: A199278 A011391 A092515 * A127454 A093602 A011469 Adjacent sequences:  A193029 A193030 A193031 * A193033 A193034 A193035 KEYWORD nonn,cons,changed AUTHOR Clark Kimberling, Jul 14 2011 STATUS approved

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Last modified January 24 18:21 EST 2022. Contains 350565 sequences. (Running on oeis4.)