%I #8 Jan 25 2024 07:54:50
%S 1,1,1,1,3,5,1,27,3,565,1,7085,25,3,11,1266205,9099507,17602325,
%T 128207979,119,1,13
%N Least number k such that pk is of minimal Hamming weight, where p is the n-th prime.
%o (PARI) min1s(p)=my(o=znorder(Mod(2,p)), v1=Set(powers(Mod(2,p),o)), v=v1, s=1); while(!setsearch(v,Mod(0,p)), v=setbinop((x,y)->x+y,v,v1); s++); s
%o a(n,p=prime(n))=my(m=min1s(p),t=p,k=2*p); while(hammingweight(t)>m, t+=k); t/p
%Y Cf. A278966, A278967, A086342.
%K nonn,more
%O 1,5
%A _Charles R Greathouse IV_, Dec 02 2016