OFFSET
1,1
COMMENTS
The first few corresponding multipliers that give three 1's are (for the numbers listed above) are 1, 3, 11, 119, 1, 13, 5, 7, 791, 87839, 247, 17970575, 3987, 8048111, 7, 49, 23, 2995944847, 5607007, 7, 2319663.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Christian Elsholtz, Almost all primes have a multiple of small Hamming weight, Bull. Aust. Math. Soc. 94 (2016), 224-235.
Eugen J. Ionascu, Florian Luca, and Thomas Merino, On the average value of the minimal Hamming multiple, arXiv:2412.10839 [math.NT], 2024. See pp. 4, 17.
Kenneth B. Stolarsky, Integers whose multiples have anomalous digital frequencies, Acta Arithmetica 38 (1980), 117-128.
MAPLE
filter:= proc(n) local S, r, j;
if not isprime(n) then return false fi;
r:= numtheory:-order(2, n);
if r::even then return false fi;
S:= {seq(2 &^ j mod n, j=1..r)};
S intersect map(t -> -t-1 mod n, S) <> {}
end proc:
select(filter, [seq(i, i=3..2000, 2)]); # Robert Israel, Jun 23 2019
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Jeffrey Shallit, Jun 20 2019
STATUS
approved