A227876 Write the decimal digits of n and take successive absolute differences; sequence is the sum of all digits at each level of the pyramid.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 2, 4, 6, 8, 10, 12, 14, 16, 18, 4, 4, 4, 6, 8, 10, 12, 14, 16, 18, 6, 6, 6, 6, 8, 10, 12, 14, 16, 18, 8, 8, 8, 8, 8, 10, 12, 14, 16, 18, 10, 10, 10, 10, 10, 10, 12, 14, 16, 18, 12, 12, 12, 12, 12, 12, 12, 14, 16, 18, 14, 14, 14, 14, 14, 14, 14, 14, 16, 18, 16, 16, 16, 16, 16, 16, 16, 16, 16, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 3, 4, 7, 10, 13, 16, 19, 22, 25, 28, 4, 3, 6, 9, 12, 15, 18, 21, 24, 27, 7, 6, 7, 8, 11, 14, 17, 20, 23, 26

Offset

0,3

Comments

A given nonnegative integer n is decomposed into its digits and the absolute differences between the digits are taken, then the differences between differences between digits (and so on, until the top of the difference pyramid is reached). The sum of the resulting digits is a(n).

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Formula

a(n)=n, if 0<=n<=9;

a(n)=n-9*floor(n/10)+|-n+11*floor(n/10)|, if 10<=n<=99;

a(n)=n-9*floor(n/10)-9*floor(n/100)+|-floor(n/10)+11*floor(n/100)|+|-n+11*floor(n/10)-10*floor(n/100)|+||-floor(n/10)+11*floor(n/100)|-|-n+11*floor(n/10)-10*floor(n/100)||, if 100<=n<=999.

Example

a(364)=19
.
____1____
__3_:_2_ --> 3+6+4+|3-6|+|6-4|+||3-6|-|6-4||=3+6+4+3+2+1=19
3_:_6_:_4

Mathematica

Join[{0}, Table[Total[Abs[Flatten[NestList[Differences[Abs[#]]&, IntegerDigits[n], IntegerLength[n]-1]]]], {n, 130}]] (* Harvey P. Dale, Mar 02 2015 *)

Prog

(PARI) a(n)=my(d=digits(n), s); while(#d, s+=sum(i=1, #d, d[i]); d=vector(#d-1, i, abs(d[i+1]-d[i]))); s \\ Charles R Greathouse IV, Oct 25 2013
(Haskell)
a227876 n = fst $ until (null . snd) h (0, a031298_row n) where
            h (s, ds) = (s + sum ds, map abs $ zipWith (-) ds $ tail ds)
-- Reinhard Zumkeller, Apr 28 2014

Crossrefs

Cf. A031298.

Sequence in context: A177895 A340184 A238986 * A276716 A189506 A173529

Adjacent sequences: A227873 A227874 A227875 * A227877 A227878 A227879

Keyword

nonn,base,easy,hear

Author

Filipi R. de Oliveira, Oct 25 2013

Status

approved