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.
0, 1, 2, 3, 5, 7, 11, 17, 19, 23
Offset: 1
Examples
0 is a term because A002275(0) = 0, which is coprime with the only other binary vector of the same length, which is 1. 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. 2 is a term because 11 is a repunit prime. 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. Counterexample: 4 is not a term because the repunit 1111 is not coprime with 1100. They are both divisible by 11.
Programs
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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
Formula
A385579(a(n)) = 1.
Comments