A180477 -id:A180477 - cp's OEIS frontend

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

Eric Angelini and Reinhard Zumkeller, Oct 27 2015

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

			a(14)=18: 18-1-8-1-8-1-8-1-8 = -18. - _Bob Selcoe_, Oct 27 2015

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Éric Angelini, Essicran Numbers, SeqFan list, Oct 27 2015.

Cf. A005349, A180477.

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)

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 *)

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

A271239 Numbers n such that n is divisible by the median of its digits.

Original entry on oeis.org

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, 90, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119

Offset: 1

José de Jesús Camacho Medina, Apr 02 2016

The first cases that are prime numbers :
a(2)=2;
a(3)=3;
a(5)=5;
a(7)=7;
a(11)=11;
a(44)=101;
a(46)=103;
a(50)=107.
The first difference from A180477 is that n = 100 is in that sequence but not here.

			72 is a member because the median of its digits (7, 2) is 9/2 and 72 is divisible by 9/2 (i.e., the ratio 72/(9/2) is an integer).

Indranil Ghosh, Table of n, a(n) for n = 1..10000

Cf. A061384, A180477.

Select[Range[500], Quiet@ Divisible[#, Median@ IntegerDigits@ #] &] (* Giovanni Resta, Apr 08 2016 *)

cp's OEIS Frontend

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

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