Least number k such that k*prime(n) has the least Hamming weight.

1, 1, 1, 1, 3, 5, 1, 27, 3, 565, 1, 7085, 25, 3, 11, 1266205, 9099507, 17602325, 128207979, 119, 1, 13, 26494256091, 1, 172961, 11147523830125, 5, 84179432287299, 2405, 145, 1, 281629680514649643, 125400505, 4246732448623781667, 126774939137440139965, 7

1

The Mathematica program has a relatively fast algorithm for computing terms.

T. D. Noe, Plot of 300 terms

T. D. Noe, Table of 300 terms

Christian Elsholtz, Almost all primes have a multiple of small Hamming weight, arXiv 1602.05974 (Feb 18 2016)

T. D. Noe, Mathematica program for computing this sequence

Cf. S000850.

nonn,base

T. D. Noe, Feb 24 2016