A064806 a(n) = n + digital root of n.

2, 4, 6, 8, 10, 12, 14, 16, 18, 11, 13, 15, 17, 19, 21, 23, 25, 27, 20, 22, 24, 26, 28, 30, 32, 34, 36, 29, 31, 33, 35, 37, 39, 41, 43, 45, 38, 40, 42, 44, 46, 48, 50, 52, 54, 47, 49, 51, 53, 55, 57, 59, 61, 63, 56, 58, 60, 62, 64, 66, 68, 70, 72, 65, 67, 69, 71

Offset: 1

Author

Reinhard Zumkeller, Oct 21 2001

Keywords

• nonn
• easy
• base

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000
• Index entries for Colombian or self numbers and related sequences.
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A010888 (digital root of n), A062028 (sum of digits of n).

Programs

Haskell

a064806 n = n + a010888 n  -- Reinhard Zumkeller, Apr 13 2013

Maple

A064806 := proc(n) return n+1 + ((n-1) mod 9): end: seq(A064806(n), n=1..100); # Nathaniel Johnston, May 04 2011

Mathematica

Table[n+Mod[n-1,9]+1,{n,70}] (* or *) LinearRecurrence[{1,0,0,0,0,0,0,0,1,-1},{2,4,6,8,10,12,14,16,18,11},70] (* Harvey P. Dale, Nov 19 2022 *)

PARI

a(n) = { n + (n - 1)%9 + 1 } \\ Harry J. Smith, Sep 26 2009

Formula

a(n) = n + A010888(n).

G.f.: -x*(9*x^9-2*x^8-2*x^7-2*x^6-2*x^5-2*x^4-2*x^3-2*x^2-2*x-2) / ((x-1)^2*(x^2+x+1)*(x^6+x^3+1)). - Colin Barker, Apr 05 2013

Sum_{n>=1} (-1)^(n+1)/a(n) = 263/315 + 8*Pi/(9*sqrt(3)) - log(2)/9 + (2*Pi/9)*(sec(Pi/18) - 4*cos(Pi/18)). - Amiram Eldar, May 12 2025