This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A325775 #16 May 25 2019 12:10:20 %S A325775 102,25,20,27,22,29,24,90,26,0,104,10,40,30,42,49,44,70,28,3,23,5,12, %T A325775 7,2,9,4,19,6,14,106,21,60,32,62,47,46,50,48,13,52,15,45,17,34,37,36, %U A325775 39,16,38,108,41,80,43,64,54,66,69,68,33,72,35,74,55,67,57,56,59,58,18,128,61,82,63,84,65,86,76,88,53,92,73,94,75,96 %N A325775 Numbers that bring back the last digit of n on its first digit, using the "boomerang protocol" explained in A308306, with no duplicate term (except the -1 terms). See the Comments and Example sections for details. %C A325775 All the nonnegative integers will appear in this sequence, except the terms of A308306. %C A325775 The "boomerang protocol" sends 1 to the left (as 1 is odd - the even digits move to the right), jumping over exactly 1 cell. To "bring back" 1 to its initial cell, the smallest integer is 102. Let's see how: %C A325775 Our initial 1 starts for instance here (dots are cells): %C A325775 ....1.... %C A325775 and ends there (S is the starting cell): %C A325775 ..1.S.... %C A325775 We have this pattern now for the "bring back" integer (S is the new start, A is the Arrival cell we must reach - which was the starting cell of 1): %C A325775 ..S.A.... %C A325775 The smallest integer starting on S and ending on A is 102: %C A325775 ..1.A.... %C A325775 0...A.... %C A325775 .2..A.... %C A325775 We see that 1 jumps to the left over 1 cell, 0 to the right over 0 cell (thus moving to this cell), 2 jumps over 2 cells and lands precisely on the Arrival cell. %C A325775 Note that many integers can "bring back" 1 in its initial cell, 120 is one of them, for instance, or 1410. %H A325775 Jean-Marc Falcoz, <a href="/A325775/b325775.txt">Table of n, a(n) for n = 1..12000</a> %e A325775 The sequence starts with 102,25,20,27,22,29,24,90,... We see that: %e A325775 a(1) = 102 means that 102 will bring 1 back in its initial cell; %e A325775 a(2) = 25 means that 25 will bring 2 back in its initial cell; %e A325775 a(3) = 20 means that 20 will bring 3 back in its initial cell; %e A325775 a(4) = 27 means that 27 will bring 4 back in its initial cell; %e A325775 a(5) = 22 means that 22 will bring 5 back in its initial cell; %e A325775 The general formula being that a(n) brings back (n) in its initial cell. %e A325775 a(100) = -1 means that 100 is a "boomerang number": it "comes back" by itself without any external help. Those numbers are listed in A308306. %Y A325775 Cf. A308306 (the "boomerang numbers") and A325776 where duplicate terms are admitted. %K A325775 sign,base %O A325775 1,1 %A A325775 _Eric Angelini_ and _Jean-Marc Falcoz_, May 20 2019