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 A325776 #12 Jun 07 2019 11:05:53 %S A325776 102,25,20,27,22,29,24,90,26,0,20,10,22,25,24,27,26,29,28,3,10,5,0,7, %T A325776 2,9,4,19,6,2,22,0,24,10,26,25,28,27,48,5,25,7,10,9,0,19,2,39,4,4,24, %U A325776 2,26,0,28,10,48,25,68,7,27,9,25,19,10,39,0,59,2,6,26,4,28,2,48,0,68,10,88,9,29,19,27,39,25,59,10,79,0,8,28,6 %N A325776 a(n) is the least nonnegative integer such that n concatenated with a(n) is a boomerang number (A308306), or -1 if n is a boomerang number. %C A325776 Old title was: "a(n) is the smallest number bringing back n on its first digit, using the 'boomerang protocol' explained in A308306." %C A325776 A similar sequence, but with no duplicate term, is A325775. %C A325776 If a(n) = -1, then n is a "boomerang number" (see A308306). %C A325776 The "boomerang protocol" sends 1 to the left (as 1 is odd), jumping over exactly 1 cell. To "bring back" 1 to its initial cell, the smallest integer is 102. Let's see how: %C A325776 Our initial 1 starts here (dots are cells): %C A325776 ....1.... %C A325776 and ends there (S is the starting cell): %C A325776 ..1.S.... %C A325776 We have this pattern now for the "bring back" integer (S is the new start, A the Arrival cell we want to reach, which was the starting cell of 1): %C A325776 ..S.A.... %C A325776 The smallest integer starting on S and ending on A is 102: %C A325776 ..1.A.... %C A325776 0...A.... %C A325776 .2..A.... %C A325776 The integer 120 does the same job, as does also 1410 - but we keep 102 as 102 is the smallest available integer. %H A325776 Jean-Marc Falcoz, <a href="/A325776/b325776.txt">Table of n, a(n) for n = 1..12000</a> %e A325776 The sequence starts with 102,25,20,27,22,29,24,90,... We see that: %e A325776 a(1) = 102 means that 102 will bring 1 back in its initial cell; %e A325776 a(2) = 25 means that 25 will bring 2 back in its initial cell; %e A325776 a(3) = 20 means that 20 will bring 3 back in its initial cell; %e A325776 a(4) = 27 means that 27 will bring 4 back in its initial cell; %e A325776 a(5) = 22 means that 22 will bring 5 back in its initial cell; %e A325776 The general rule being that a(n) is the smallest number bringing back n in its initial cell. %e A325776 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. %e A325776 a(1) is not 0, since even though the least boomerang number beginning with 1 is 100, leading zeroes are not allowed. - _Charlie Neder_, Jun 03 2019 %Y A325776 Cf. A308306 (the "boomerang numbers"), and A325775 (where duplicate terms are not admitted). %K A325776 sign,base %O A325776 1,1 %A A325776 _Eric Angelini_ and _Jean-Marc Falcoz_, May 20 2019 %E A325776 New title from _Charlie Neder_, Jun 03 2019