A308732 - OEIS

A308732

Primes p such that the smallest possible number of 1's in binary representation of a multiple of p equals 3.

7, 23, 47, 71, 73, 79, 103, 151, 167, 191, 199, 239, 263, 271, 311, 337, 359, 367, 383, 439, 463, 479, 487, 503, 599, 607, 631, 647, 719, 727, 743, 751, 823, 839, 863, 887, 919, 937, 967, 983, 991, 1031, 1039, 1063, 1087, 1151, 1223, 1231, 1279, 1289, 1303

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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

C. Elsholtz, Almost all primes have a multiple of small Hamming weight, Bull. Aust. Math. Soc. 94 (2016), 224-235.

K. 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: