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 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. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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: A297233 A177895 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

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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)