OFFSET
0,3
COMMENTS
Instead of (a(n) mod 10) one might say "the last (decimal) digit of a(n)".
Apart from the initial term, the first differences form the periodic sequence (2,4,8,6)[repeated].
Without the final "+ 1" and starting with 1, one gets A102039: Indeed, the last digit cycles through 2,4,8,6 and therefore the sequence never becomes constant.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
FORMULA
a(n) = 5*n-6+cos(n*Pi/2)+2*sin(n*Pi/2), for n>0. - Giovanni Resta, Jan 15 2014
From Colin Barker, Jan 16 2014: (Start)
a(n) = -6+(1/2+i)*(-i)^n+(1/2-i)*i^n+5*n for n>0 where i=sqrt(-1).
a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4) for n>4.
G.f.: x*(5*x^3+3*x^2+x+1) / ((x-1)^2*(x^2+1)). (End)
MATHEMATICA
NestList[#+Mod[#, 10]+1&, 0, 80] (* or *) Join[{0}, LinearRecurrence[{2, -2, 2, -1}, {1, 3, 7, 15}, 80]] (* Harvey P. Dale, Dec 21 2014 *)
PROG
(PARI) print1(a=0); for(i=1, 99, print1(", "a+=a%10+1))
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Jan 14 2014
STATUS
approved