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A235699
a(n+1) = a(n) + (a(n) mod 10) + 1, a(0) = 0.
1
0, 1, 3, 7, 15, 21, 23, 27, 35, 41, 43, 47, 55, 61, 63, 67, 75, 81, 83, 87, 95, 101, 103, 107, 115, 121, 123, 127, 135, 141, 143, 147, 155, 161, 163, 167, 175, 181, 183, 187, 195, 201, 203, 207, 215, 221, 223, 227, 235, 241, 243, 247, 255, 261, 263, 267, 275, 281, 283, 287, 295, 301, 303, 307, 315, 321, 323, 327, 335, 341, 343, 347, 355
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.
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