A351149 a(n) is the least exponent k such that the Hamming weight of n^(k+1) is not greater than the Hamming weight of n^k.

1, 1, 1, 1, 3, 1, 1, 1, 3, 3, 5, 1, 7, 1, 1, 1, 3, 3, 4, 3, 2, 5, 1, 1, 4, 7, 5, 1, 5, 1, 1, 1, 3, 3, 7, 3, 4, 4, 3, 3, 5, 2, 5, 5, 3, 1, 1, 1, 5, 4, 7, 7, 2, 5, 3, 1, 3, 5, 2, 1, 3, 1, 1, 1, 3, 3, 4, 3, 5, 7, 3, 3, 3, 4, 3, 4, 3, 3, 1, 3, 5, 5, 3, 2, 3, 5, 11

Offset: 1

Author

Hugo Pfoertner, Feb 07 2022

Keywords

• nonn

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A094694, A211201, A231897.

Programs

Mathematica

a[n_] := Module[{k = 1}, While[DigitCount[n^k, 2, 1] < DigitCount[n^(k + 1), 2, 1], k++]; k]; Array[a, 100] (* Amiram Eldar, Feb 07 2022 *)

PARI

for(n=1,87, for(k=1,oo, my(hw1=hammingweight(n^k), hw2=hammingweight(n^(k+1))); if(hw2<=hw1, print1(k,", "); break)))

Python

def A351149(n):
    k = 1
    while bin(n**k)[2:].count("1") < bin(n**(k+1))[2:].count("1"): k += 1
    return(k)
print([A351149(n) for n in range(1, 88)]) # Karl-Heinz Hofmann, Feb 07 2022