cp's OEIS Frontend

A308306 Boomerang numbers: their last digit "comes back" to occupy the place of their first digit (see the Comments section for the explanation).

%I A308306 #21 May 25 2019 11:49:03
%S A308306 100,203,225,230,247,252,269,274,296,302,320,405,427,449,450,472,494,
%T A308306 504,522,540,607,629,670,692,706,724,742,760,809,890,908,926,944,962,
%U A308306 980,1012,1021,1034,1043,1056,1065,1078,1087,1102,1120,1201,1210,1223,1232,1245,1254,1267,1276,1289,1298,1304,1322,1340,1403,1425,1430
%N A308306 Boomerang numbers: their last digit "comes back" to occupy the place of their first digit (see the Comments section for the explanation).
%C A308306 Take 2019; start with 2; jump over 2 cells to the right (as the even digits always move to the right); write 0 on the landing cell; jump over 0 cell to the right (which is the same as moving to the next cell to the right) and write 1 on the landing cell; as 1 is odd, jump over 1 cell to the left; write 9 on the landing cell; jump now over 9 cells to the left and mark A (for "Arrival") on the landing cell. The result will look like this (a dot is a cell): A.......2.901
%C A308306 As this A cell is not the same as the starting one (with "2"), 2019 is not a boomerang number. If we had taken 2011, we would have come back on the starting 2, like this:
%C A308306 2011
%C A308306 2..0
%C A308306 2..01
%C A308306 2.101
%C A308306 A.101
%C A308306 This is why 2011 is in the sequence and 2019 not.
%C A308306 Note that a cell, empty or not, is only a stopover: it can be used several times by different digits.
%C A308306 There are 263499 boomerang numbers < 10^7.
%C A308306 A boomerang number is easy to find, knowing the hereunder definition:
%C A308306 Integers B such that (the number of even digits + the sum of those) = (the number of odd digits + the sum of those).
%C A308306 Note: this sequence is not related to A256174 ("Boomerang fractions").
%H A308306 Jean-Marc Falcoz, <a href="/A308306/b308306.txt">Table of n, a(n) for n = 1..28444</a>
%e A308306 7308403 is a boomerang number as we have 4 even digits with sum 12 (4+12=16) and 3 odd digits with sum 13 (3+13=16).
%Y A308306 CF. A325775 and A325776 which play with the same concept.
%K A308306 base,nonn
%O A308306 1,1
%A A308306 _Eric Angelini_ and _Jean-Marc Falcoz_, May 19 2019