A308730 - OEIS

%I #14 Jul 06 2019 06:09:07

%S 2,3,7,89,31,13367,127,2099863,178481

%N Smallest prime p for which n is the least number of 1's in the base-2 representation of a multiple of p.

%C It is not known if a(n) actually exists for all n.  If there are infinitely many Mersenne primes, then a(n) is defined for infinitely many n.

%C The corresponding multipliers for n = 1,2,...,7 are 1,1,1,1,1,5,1,1,1.   (Computations done by Leon Witzman.)

%H K. B. Stolarsky, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa38/aa3825.pdf">Integers whose multiples have anomalous digital frequencies</a>, Acta Arithmetica 38 (1980), 117-128, DOI:<a href="https://doi.org/10.4064/aa-38-2-117-128">10.4064/aa-38-2-117-128</a>.

%F A086342(a(n)) = n. - _Rémy Sigrist_, Jul 06 2019

%Y Cf. A086342, A278966.

%K nonn,base,more

%O 1,1

%A _Jeffrey Shallit_, Jun 20 2019