Barak Manos - cp's OEIS frontend

User: Barak Manos

Barak Manos has authored 2 sequences.

A381754 Numbers k such that k and 3*k have the same number of zeros in their binary expansions.

0, 1, 2, 4, 8, 16, 19, 32, 35, 38, 39, 53, 64, 67, 70, 71, 76, 78, 79, 101, 105, 106, 117, 128, 131, 134, 135, 140, 142, 143, 152, 156, 158, 159, 197, 201, 202, 209, 210, 212, 229, 233, 234, 245, 256, 259, 262, 263, 268, 270, 271, 280, 284, 286, 287, 301, 304

Offset: 1

Barak Manos, Mar 06 2025

If n is in the sequence, so is 2n, hence the sequence is infinite. - Charles R Greathouse IV, Mar 06 2025

This sequence corresponds to the numbers m such that A381934(m) <= 3. - Rémy Sigrist, Mar 12 2025

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A023416, A077459, A381934.

filter:= proc(n) numboccur(0,convert(n,base,2)) = numboccur(0,convert(3*n,base,2)) end proc:
select(filter, [$0..400]); # Robert Israel, Apr 07 2025

Select[Range[0, 320], Equal @@ DigitCount[{#, 3*#}, 2, 0] &] (* Amiram Eldar, Mar 06 2025 *)

nz(n) = if(n == 0, 1, 1+logint(n, 2) - hammingweight(n))
is(n)=nz(n)==nz(3*n) \\ Charles R Greathouse IV, Mar 06 2025

def ok(n): return bin(n).count('0') == bin(n * 3).count('0')

A381762 Numbers k such that S(k) sets a new record, where S(k) denotes the sum of the reciprocals of odd elements in the Collatz sequence which starts at k.

Original entry on oeis.org

1, 3, 7, 9, 559, 745, 993

Offset: 1

Barak Manos, Mar 06 2025

This sequence is conjectured to be finite.

Cf. A304174.

Cf. A127789.

f[n_] := Total[1/Select[NestWhileList[If[OddQ[#], 3*# + 1, #/2] &, n, # > 1 &], OddQ]]; seq[lim_] := Module[{s = {}, fm = 0, f1}, Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]], {n, 1, lim}]; s]; seq[1000] (* Amiram Eldar, Mar 06 2025 *)

from fractions import Fraction
def S(n):
    arr = []
    while True:
        n //= (n - (n & (n - 1)))
        arr.append(n)
        if n == 1:
            break
        n = 3 * n + 1
    return sum(Fraction(1, x) for x in arr)
m = 0
for n in range(1, 1000):
    k = S(n)
    if m < k:
        m = k
        print(n)

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User: Barak Manos

A381754 Numbers k such that k and 3*k have the same number of zeros in their binary expansions.

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