A087994 -id:A087994 - cp's OEIS frontend

A087993 Numbers k for which the quotient q(k)=(k+rev(k))/abs(k-rev(k)) is an integer.

45, 54, 495, 594, 4356, 4545, 4995, 5454, 5895, 5985, 5994, 6534, 10890, 19602, 20691, 29403, 30492, 39204, 40293, 43956, 45045, 49005, 49995, 50094, 54054, 59994, 65934, 68607, 70686, 77319, 91377, 109890, 197802, 208791, 296703, 307692

Offset: 1

Labos Elemer, Oct 08 2003

			n = 45, rev(n) = 54, q = 99/9 = 9 integer;
n = 934065, rev(n) = 560434, q = 1494504/373626 = 4, integer.

Giovanni Resta, Table of n, a(n) for n = 1..500

Cf. A087994 (the quotients), A118959.

rev[n_] := FromDigits@ Reverse@ IntegerDigits@ n; Select[Range[10^5], # != (r = rev[#]) && Mod[# + r, # - r] == 0 &] (* Giovanni Resta, May 14 2017 *)

A087996 Residues when (n+rev[n]) is divided by abs(n-rev[n]); zero if n=rev[n] (when n is palindromic), or when the quotient is an integer (see A087993).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 6, 8, 1, 30, 32, 34, 36, 38, 4, 6, 0, 1, 12, 23, 16, 9, 2, 58, 6, 8, 1, 0, 5, 16, 18, 2, 31, 24, 8, 1, 12, 5, 0, 0, 2, 13, 24, 8, 10, 30, 23, 16, 0, 0, 4, 6, 8, 10, 12, 32, 16, 18, 2, 4, 0, 8, 10, 3, 14, 34, 9, 2, 13, 6, 8, 0, 3, 14, 16, 36, 2, 31, 24, 8, 10, 3, 0, 7

Offset: 1

Labos Elemer, Oct 08 2003

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A087993, A087994.

Table[With[{rev=IntegerReverse[n]},If[PalindromeQ[n],0,Mod[n+rev,Abs[n-rev]]]],{n,90}] (* Harvey P. Dale, Aug 23 2025 *)

a(n) = Mod[n+rev(n), abs[n-rev(n)]] if n is non-palindromic or is non-integer; a(n)=0 otherwise.

cp's OEIS Frontend

A087993 Numbers k for which the quotient q(k)=(k+rev(k))/abs(k-rev(k)) is an integer.

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