A072830 Absolute value of 2*b(n)-9*n, where b(n) = accumulative sum of the greatest digit of n minus the least digit of n (A037904).

9, 18, 27, 36, 45, 54, 63, 72, 81, 88, 97, 104, 109, 112, 113, 112, 109, 104, 97, 102, 109, 118, 125, 130, 133, 134, 133, 130, 125, 128, 133, 140, 149, 156, 161, 164, 165, 164, 161, 162, 165, 170, 177, 186, 193, 198, 201, 202, 201, 200, 201, 204, 209, 216

Offset: 1

Author

Benoit Cloitre and Robert G. Wilson v, Aug 09 2002

Keywords

• nonn
• base

Crossrefs

Cf. A037904.

Programs

Mathematica

f[n_] := Block[{d = IntegerDigits[n]}, Max[d] - Min[d]]; b[n_] := b[n] = b[n - 1] + f[n]; b[1] = 0; a[n_] := a[n] = Abs[2b[n] - 9*n]; Table[ a[n], {n, 1, 65}]
gdmld[n_]:=Module[{idn=IntegerDigits[n]},Max[idn]-Min[idn]]; Module[ {nn=60,gd}, gd=Accumulate[gdmld/@Range[nn]];Abs[ 2*Last[#]- 9*First[ #]]&/@Thread[{Range[nn],gd}]]

Formula

Let b(n) = sum( A037904(k), {k=1..n}), a(n) = |2*b(n) - 9*n|.

Extensions

Definition clarified by Harvey P. Dale, May 21 2014