A133446 Decimal expansion of the number c such that the solution to the differential functional equation f'(x) = f(x-1) + f(x-2) is c^x.

2, 0, 5, 8, 2, 9, 5, 6, 0, 8, 2, 3, 5, 1, 7, 3, 9, 1, 0, 6, 7, 8, 6, 5, 2, 3, 9, 5, 8, 9, 8, 6, 4, 5, 1, 8, 6, 8, 8, 4, 1, 7, 1, 9, 5, 4, 9, 4, 0, 7, 8, 9, 4, 9, 6, 1, 1, 4, 7, 8, 9, 6, 0, 6, 1, 0, 5, 2, 4, 6, 3, 6, 6, 0, 5, 5, 4, 5, 1, 6, 2, 1, 4, 7, 7, 4, 1, 3, 5, 0, 9, 2, 1, 4, 1, 8, 5, 0, 0, 5, 7, 4, 9, 5, 4

Offset

1,1

Comments

This is related to phi, as phi^x is the solution to f(x) = f(x-1) + f(x-2).

Links

Table of n, a(n) for n=1..105.

Formula

f(x-1) + f(x-2) = f'(x), f(x) = 2.058295608^x.

Maple

solve(ln(x)*x^2=x+1)
read("transforms3") ; Digits := 120 ; x := 2.0 ; for l from 1 to 10 do x := x-(x*log(x)-1-1/x)/(2*log(x)+1-1/x) ; x := evalf(x) ; end do; CONSTTOLIST(x) ; # R. J. Mathar, Mar 23 2010

Mathematica

digits = 105; c /. FindRoot[1 + 1/c == c*Log[c], {c, 2}, WorkingPrecision -> digits+5] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Mar 05 2013 *)

Crossrefs

Sequence in context: A111352 A173343 A334059 * A011122 A329960 A085009

Adjacent sequences: A133443 A133444 A133445 * A133447 A133448 A133449

Keyword

cons,nonn

Author

Cameron Davidson-Pilon (see_dee_pee(AT)hotmail.com), Nov 26 2007

Extensions

More digits from R. J. Mathar, Mar 23 2010

Status

approved