A055263 a(n) = Sum of digits of (n + a(n-1)).

0, 1, 3, 6, 1, 6, 3, 1, 9, 9, 10, 3, 6, 10, 6, 3, 10, 9, 9, 10, 3, 6, 10, 6, 3, 10, 9, 9, 10, 12, 6, 10, 6, 12, 10, 9, 9, 10, 12, 6, 10, 6, 12, 10, 9, 9, 10, 12, 6, 10, 6, 12, 10, 9, 9, 10, 12, 15, 10, 15, 12, 10, 9, 9, 10, 12, 15, 10, 15, 12, 10, 9, 9, 10, 12, 15, 10, 15, 12, 10, 9, 9, 10

Offset: 0

Author

Henry Bottomley, May 08 2000

Keywords

• base
• easy
• nonn

Comments

If n=0 or 8 mod 9, then a(n)=0 mod 9; if n=1, 4 or 7 mod 9, then a(n)=1 mod 9; if n=2 or 6 mod 9, then a(n)=3 mod 9; if n=3 or 5 mod 9, then a(n)=6 mod 9.

Examples

			a(13)=10 because a(12)=6, 13 + 6 = 19 and 1 + 9 = 10.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A055262, A055264.

Programs

Mathematica

nxt[{n_,a_}]:={n+1,Total[IntegerDigits[n+a+1]]}; Transpose[NestList[nxt,{0,0},90]][[2]] (* Harvey P. Dale, Aug 11 2016 *)

Formula

a(n) = A007953(A055262(n)) = A007953(n + a(n-1)).

Extensions

More terms from Paolo P. Lava, Jul 31 2007