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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.
0
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).
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
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