A351835 Smallest odious number k (member of A000069) such that k*n is also odious.

1, 1, 7, 1, 7, 7, 1, 1, 13, 7, 1, 7, 1, 1, 19, 1, 21, 13, 1, 7, 1, 1, 7, 7, 1, 1, 13, 1, 7, 19, 1, 1, 37, 21, 1, 13, 1, 1, 7, 7, 1, 1, 7, 1, 19, 7, 1, 7, 1, 1, 7, 1, 11, 13, 1, 1, 25, 7, 1, 19, 1, 1, 67, 1, 69, 37, 1, 21, 1, 1, 11, 13, 1, 1, 19, 1, 7, 7, 1, 7

Offset

1,3

Comments

All terms are odd since if 2*j and 2*j*n are both odious, then so are j and j*n. - Michael S. Branicky, Feb 21 2022

Links

Table of n, a(n) for n=1..80.

Example

For n = 5, we have 5*7 = 35, and both 7 and 35 are odious, and no smaller odious multiple of 5 works.

Mathematica

odiousQ[n_] := OddQ[DigitCount[n, 2, 1]]; a[n_] := Module[{k = 1}, While[!odiousQ[k] || !odiousQ[k*n], k++]; k]; Array[a, 100] (* Amiram Eldar, Feb 21 2022 *)

Prog

(Python)
def od(n): return bin(n).count("1")%2 == 1
def a(n):
    k = 1
    while not (od(k) and od(k*n)): k += 1
    return k
print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Feb 21 2022
(PARI) isodious(m) = hammingweight(m) % 2;
a(n) = my(k=1); while (!isodious(k) || !isodious(k*n), k++); k; \\ Michel Marcus, Feb 22 2022

Crossrefs

Cf. A000069, A351836 (analog for the evil numbers A001969).

Cf. A178757 (where k is not necessarily odious).

Sequence in context: A160798 A033953 A295872 * A010772 A199732 A293238

Adjacent sequences: A351832 A351833 A351834 * A351836 A351837 A351838

Keyword

nonn,base

Author

Jeffrey Shallit, Feb 21 2022

Status

approved