A235699 a(n+1) = a(n) + (a(n) mod 10) + 1, a(0) = 0.

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

Author

M. F. Hasler, Jan 14 2014

Keywords

• nonn
• base
• easy

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).

Crossrefs

Cf. A102039, A235698, A045844.

Programs

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 *)

PARI

print1(a=0);for(i=1,99,print1(","a+=a%10+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)