OFFSET
0,1
COMMENTS
O. M. Cain proves that the number of consecutive zeros in the decimal expansion of 5^(n+2^n+2), that is 5^a(n+1), is nondecreasing and grows to infinity as m gets bigger. See link. - Michel Marcus, Nov 07 2019
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
O. M. Cain, The Exceptional Selfcondensability of Powers of Five, arXiv:1910.13829 [math.HO], 2019. See Theorem 10.4. p. 13.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1040
Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
FORMULA
G.f.: (-2 + 5*x - 3*x^2 + x^3)/(-1+2*x)/(-1+x)^2
Recurrence: {a(3)=8, a(2)=5, a(1)=3, a(0)=2, 2*a(n)-a(n+1)-n=0}.
MAPLE
spec := [S, {S=Union(Sequence(Prod(Sequence(Z), Z)), Prod(Sequence(Z), Sequence(Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
MATHEMATICA
CoefficientList[Series[(-2+5*x-3*x^2+x^3)/(-1+2*x)/(-1+x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 22 2012 *)
Join[{2}, Table[1+2^(n-1)+n, {n, 40}]] (* or *) LinearRecurrence[{4, -5, 2}, {2, 3, 5, 8}, 40] (* Harvey P. Dale, Feb 10 2018 *)
PROG
(Magma) I:=[2, 3, 5, 8]; [n le 4 select I[n] else 4*Self(n-1)-5*Self(n-2)+2*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 22 2012
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from James A. Sellers, Jun 05 2000
STATUS
approved