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

1,3

Comments

It appears that all nonzero terms in this sequence are divisible by 3 unless n is divisible by 9.

Links

Table of n, a(n) for n=1..88.

Formula

a(n) = A007953(A036275(n)).

Example

1/7 = 0.142857142857142857... and digit-cycle is 142857, the sum of these integers is 27 so a(7)=27.

Mathematica

a[n_] := Block[{d = RealDigits[1/n][[1, -1]]}, If[ IntegerQ@d, 0, Plus @@ d]]; Array[a, 100] (* Giovanni Resta, May 15 2016 *)

Crossrefs

Cf. A036275.

Sequence in context: A285311 A285131 A110620 * A060284 A036275 A131436

Adjacent sequences: A270389 A270390 A270391 * A270393 A270394 A270395

Keyword

base,nonn,easy

Author

Neville Styles, Mar 16 2016

Status

approved