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

0,3

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).

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

Example

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.

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 *)

Prog

(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
(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

Crossrefs

Cf. A098488, A006068.

Sequence in context: A033865 A364274 A118764 * A057717 A183222 A063742

Adjacent sequences: A226131 A226132 A226133 * A226135 A226136 A226137

Keyword

base,easy,nonn

Author

Paul Tek, May 27 2013

Status

approved