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 A351243 #25 Jan 12 2024 07:55:49 %S A351243 247,277,967,977,1211,1219,1895,1937,1951,1961,2183,2191,2911,2921, %T A351243 3029,3641,3649 %N A351243 Counterexamples to a conjecture of Selfridge and Lacampagne. %C A351243 The conjecture was that every natural number k not divisible by 3 can be written as the quotient of two terms chosen from A147991. %C A351243 For every specific k, the problem of representing k as the quotient of two terms of A147991 can be decided by using a queue-based breadth-first search algorithm on the transition diagram of a finite automaton that on input j in base 3 computes j*k and checks to see if both j and j*k are in A147991. %C A351243 It is not known if there are infinitely many counterexamples to the conjecture, but perhaps 3^m+4, for m >= 5 and odd, are. %D A351243 R. K. Guy, Unsolved Problems in Number Theory, Springer, 2004. In Section F31, the conjecture of Selfridge and Lacampagne is mentioned, and it is stated that Don Coppersmith found the counterexample 247. %H A351243 James Haoyu Bai, Joseph Meleshko, Samin Riasat, and Jeffrey Shallit, <a href="http://math.colgate.edu/~integers/w96/w96.pdf">Quotients of Palindromic and Antipalindromic Numbers</a>, INTEGERS 22 (2022), #A96. %H A351243 J. H. Loxton and A. J. van der Poorten, <a href="https://doi.org/10.4064/aa-49-2-193-203">An Awful Problem About Integers in Base Four</a>, Acta Arithmetica, volume 49, 1987, pages 193-203. In section 7, Selfridge and Lacampagne ask whether every k != 0 (mod 3) is the quotient of two terms of this sequence. %Y A351243 Cf. A147991. %K A351243 nonn,base,more %O A351243 1,1 %A A351243 _Jeffrey Shallit_, Feb 05 2022