A226134 The partial digital sums of n from left to right mod 10 give the digits of a(n).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 10, 22, 23, 24, 25, 26, 27, 28, 29, 20, 21, 33, 34, 35, 36, 37, 38, 39, 30, 31, 32, 44, 45, 46, 47, 48, 49, 40, 41, 42, 43, 55, 56, 57, 58, 59, 50, 51, 52, 53, 54, 66, 67, 68, 69, 60, 61, 62, 63, 64, 65, 77, 78, 79, 70, 71, 72, 73, 74, 75, 76, 88, 89, 80, 81, 82, 83, 84, 85, 86, 87

Offset: 0

Author

Paul Tek, May 27 2013

Keywords

• base
• easy
• nonn

Comments

Inverse permutation to A098488.

Analogous to A006068 for the decimal base.

For any n, the sequence n, a(n), a(a(n)), a(a(a(n))),... is periodic.

The periods encountered between 0 and 10^6 are:

- 1 (n=0),

- 10 (n=10),

- 5 (n=20),

- 2 (n=50),

- 20 (n=100),

- 4 (n=500),

- 40 (n=10000),

- 8 (n=50000),

- 200 (n=100000),

- 25 (n=200000),

- 50 (n=200010),

- 100 (n=200100).

Examples

			1       = 1 mod 10.
1+9     = 0 mod 10.
1+9+5   = 5 mod 10.
1+9+5+4 = 9 mod 10.
Hence, a(1954)=1059.
		

Links

• Paul Tek, Table of n, a(n) for n = 0..10000
• Paul Tek, Parity of the decimal digits of n, a(n), a(a(n)), a(a(a(n))),... with n=200!
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A098488, A006068.

Programs

Haskell

a226134 = foldl (\v d -> 10*v+d) 0 . scanl1 (\d x -> (x+d) `mod` 10) .
          map (read . return) . show :: Int -> Int
-- Reinhard Zumkeller, Jun 03 2013

Mathematica

Table[With[{idn=IntegerDigits[n]},FromDigits[Table[Mod[Total[Take[idn,i]],10],{i,Length[idn]}]]],{n,0,90}] (* Harvey P. Dale, Mar 08 2015 *)

PARI

a(n)=my(b); if(n<10, return(n), b=a(n\10); return(10*b + (b+n)%10))

PARI

a(n) = my(v=digits(n)); for(i=2,#v, v[i]=(v[i]+v[i-1])%10); fromdigits(v); \\ Kevin Ryde, May 15 2020