A136318 -id:A136318 - cp's OEIS frontend

A212314 Numbers m such that B(m^3) = 3*B(m), where B(m) is the binary weight of m (A000120).

0, 5, 9, 10, 17, 18, 20, 33, 34, 36, 39, 40, 49, 65, 66, 68, 69, 72, 78, 80, 98, 105, 129, 130, 132, 135, 136, 138, 144, 156, 160, 169, 196, 199, 209, 210, 229, 257, 258, 260, 263, 264, 270, 272, 276, 277, 288, 291, 297, 312, 313, 320, 338, 359, 365, 392, 395, 398, 418

Offset: 1

Alex Ratushnyak, Oct 24 2013

2*k is a term if and only if k is a term. - Robert Israel, Nov 06 2022

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

Cf. A000120, A077436, A083567, A118655, A212315.

Includes A136318.

select(n -> convert(convert(n^3,base,2),`+`) = 3*convert(convert(n,base,2),`+`), [$0..1000]); # Robert Israel, Nov 06 2022

isok(m) = hammingweight(m^3) == 3*hammingweight(m); \\ Michel Marcus, Nov 06 2022

import math
for n in range(10000):
    c1 = c2 = 0
    t = n
    while t:
        c1+=t&1
        t>>=1
    t = n*n*n
    while t:
        c2+=t&1
        t>>=1
    if c1*3==c2: print(str(n), end=',')

s = lambda n: sum((n^3).digits(2)) - 3*sum(n.digits(2))
[n for n in (0..418) if s(n)==0]  # Peter Luschny, Oct 24 2013

A000120(a(n)^3) = A000120(a(n)) * 3.

A382631 Integers whose binary representation contains exactly four 1's, no two 1's being adjacent.

Original entry on oeis.org

85, 149, 165, 169, 170, 277, 293, 297, 298, 325, 329, 330, 337, 338, 340, 533, 549, 553, 554, 581, 585, 586, 593, 594, 596, 645, 649, 650, 657, 658, 660, 673, 674, 676, 680, 1045, 1061, 1065, 1066, 1093, 1097, 1098, 1105, 1106, 1108, 1157, 1161, 1162, 1169, 1170

Offset: 1

Chai Wah Wu, Apr 07 2025

Subsequence of A003714 and of A014312.

			85 = 1010101_2, 1066 = 10000101010_2.

Cf. A003714, A014312, A136318, A173589.

def A382631_gen(): # generator of terms
    n = 15
    yield 85
    while True: yield int(bin(n:=n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b)[2:].replace('1','01'),2)
A382631_list = list(islice(A382631_gen(),30))

cp's OEIS Frontend

A212314 Numbers m such that B(m^3) = 3*B(m), where B(m) is the binary weight of m (A000120).

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