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 A385537 #29 Jul 07 2025 17:21:16 %S A385537 0,1,2,3,5,7,11,17,19,23 %N A385537 Indices k such that the repunit (10^k-1)/9 is coprime with any other nonzero binary vector of the same length in base 10. %C A385537 k is a term iff A378511(k) <= 1. %C A385537 k is a term iff A385539(k) <= 1. %C A385537 a(n) contains all indices of prime repunits A004023 as a subsequence. %C A385537 If A378199(k) <= 1, then k is a term in this sequence, however the inverse is not true. The smallest counterexample is k = 19. %C A385537 a(11) >= 59. - _Michael S. Branicky_, Jul 03 2025 %F A385537 A385579(a(n)) = 1. %e A385537 0 is a term because A002275(0) = 0, which is coprime with the only other binary vector of the same length, which is 1. %e A385537 1 is a term because A002275(1) = 1, there are no other nonzero binary vectors of length 1, and any statement about the elements of an empty set is true. %e A385537 2 is a term because 11 is a repunit prime. %e A385537 3 is a term because 111=3*37 is coprime with all other nonzero binary vectors of length 3, which are 001, 010, 011, 100, 101, 110. None of them is divisible by 3 or 37. %e A385537 Counterexample: 4 is not a term because the repunit 1111 is not coprime with 1100. They are both divisible by 11. %o A385537 (PARI) isok(k) = my(x=(10^k-1)/9); for (i=1, 2^k-2, if (gcd(fromdigits(binary(i)), x) != 1, return(0)); ); return(1); \\ _Michel Marcus_, Jul 03 2025 %Y A385537 Cf. A378199, A378511, A378761, A385539, A385579. %Y A385537 Supersequence of A004023. %K A385537 nonn,base,more %O A385537 1,3 %A A385537 _Dmytro Inosov_, Jul 02 2025