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

Author

Filipi R. de Oliveira, Oct 25 2013

Keywords

• nonn
• base
• easy
• hear

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).

Examples

			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
		

Links

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

Crossrefs

Cf. A031298.

Programs

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

Mathematica

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

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

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.