A263808 Numbers k such that the iterated subtraction of the decimal digits eventually reaches -k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, 20, 21, 22, 24, 27, 30, 33, 36, 40, 42, 44, 45, 48, 50, 51, 54, 55, 60, 63, 66, 70, 72, 77, 80, 81, 84, 88, 89, 90, 98, 99, 100, 101, 102, 105, 108, 110, 111, 112, 113, 114, 116, 117, 120, 123, 124, 126, 128

Offset

1,2

Comments

A180477 is a subsequence of this sequence. - Hans Havermann, Oct 27 2015

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Éric Angelini, Essicran Numbers, SeqFan list, Oct 27 2015.

Example

a(14)=18: 18-1-8-1-8-1-8-1-8 = -18. - Bob Selcoe, Oct 27 2015

Mathematica

eQ[n_] := Block[{d = IntegerDigits@ n}, MemberQ[Accumulate@ d ~Prepend~ 0, Mod[2*n, Total@ d]]]; Select[Range@ 128, eQ] (* Giovanni Resta, Oct 27 2015 *)

Prog

(Haskell)
a263808 n = a263808_list !! (n-1)
a263808_list = filter essicran [1..] where
   essicran x = last (takeWhile (>= -x) es) == -x where
     es = scanl (-) x (cycle $ map (read . return) $ show x)
(PARI) is(n)=my(d=digits(n), t, S=vector(#d-1, i, t+=d[i])); t=2*n%vecsum(d); t==0 || setsearch(S, d) \\ Charles R Greathouse IV, Oct 28 2015

Crossrefs

Cf. A005349, A180477.

Sequence in context: A050607 A238368 A342164 * A180477 A271239 A083970

Adjacent sequences: A263805 A263806 A263807 * A263809 A263810 A263811

Keyword

nonn,base

Author

Eric Angelini and Reinhard Zumkeller, Oct 27 2015

Status

approved