A270392 The sum of the digits in the periodic part of the decimal expansion of 1/n.
0, 0, 3, 0, 0, 6, 27, 0, 1, 0, 9, 3, 27, 27, 6, 0, 72, 5, 81, 0, 27, 9, 99, 6, 0, 27, 10, 27, 126, 3, 54, 0, 3, 72, 27, 7, 9, 81, 18, 0, 18, 27, 90, 9, 2, 99, 207, 3, 189, 0, 69, 27, 63, 14, 9, 27, 81, 126, 261, 6, 270, 54, 24, 0, 27, 6, 144, 72, 96, 27, 126, 8, 36, 9, 3, 81, 27, 18, 54, 0, 37, 18, 171, 27, 72, 99, 123, 9
Offset: 1
Examples
1/7 = 0.142857142857142857... and digit-cycle is 142857, the sum of these integers is 27 so a(7)=27.
Crossrefs
Cf. A036275.
Programs
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Mathematica
a[n_] := Block[{d = RealDigits[1/n][[1,-1]]}, If[ IntegerQ@d, 0, Plus @@ d]]; Array[a, 100] (* Giovanni Resta, May 15 2016 *)
Comments