A102029 -id:A102029 - cp's OEIS frontend

A178065 Number of 1's in binary representation of n-th semiprime.

1, 2, 2, 2, 3, 4, 3, 3, 3, 3, 2, 2, 3, 3, 4, 4, 3, 4, 5, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 5, 5, 5, 6, 4, 6, 5, 5, 6, 5, 5, 6, 2, 3, 3, 4, 4, 5, 3, 3, 5, 5, 6, 3, 4, 4, 4, 4, 6, 5, 6, 3, 4, 4, 5, 5, 5, 4, 5, 5, 6, 5, 5, 6, 6, 4, 6, 6, 7, 6, 7, 7, 3, 3, 3, 4, 3, 4, 6, 3, 4, 5, 4, 5, 5, 5, 6, 4, 5, 5, 7, 3, 4, 4, 5

Offset: 1

Juri-Stepan Gerasimov, May 18 2010

			a(1)=1 because the first semiprime is 4 = 100_2.
a(2)=2 because the second semiprime is 6 = 110_2.

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

Cf. A001358, A014499, A102029.

N:= 10^3: # for semiprimes <= N
P:= select(isprime,[2,seq(i,i=3..N/2,2)]):
SP:= sort(select(`<=`,[seq(seq(P[i]*P[j],j=1..i),i=1..nops(P))],N)):
map(t -> convert(convert(t,base,2),`+`), SP); # Robert Israel, Feb 02 2025

s={};Do[If[PrimeOmega[n]==2,AppendTo[s,Total[IntegerDigits[n,2]]]],{n,400}];s (* James C. McMahon, Jan 02 2025 *)

lista(nn) = {for (n=2, nn, if (bigomega(n)==2, print1(norml2(binary(n)), ", ")););} \\ Michel Marcus, Jun 05 2013

a(56) corrected by R. J. Mathar, May 23 2010

A354480 a(n) is the smallest decimal palindrome with Hamming weight n (i.e., with exactly n 1's when written in binary).

Original entry on oeis.org

0, 1, 3, 7, 77, 55, 111, 191, 383, 767, 5115, 11711, 15351, 30703, 81918, 97279, 744447, 978879, 1570751, 3665663, 8387838, 66911966, 66322366, 132111231, 199212991, 389545983, 939474939, 3204444023, 3220660223, 11542724511, 34258485243, 33788788733, 34292629243

Offset: 0

Ilya Gutkovskiy, Jun 02 2022

Cf. A000120, A000225, A002113, A061712, A062388, A089226, A089998, A089999, A102029, A114477.

from itertools import count, islice, product
def pals(startd=1): # generator for base-10 palindromes
    for d in count(startd):
        for p in product("0123456789", repeat=d//2):
            if d//2 > 0 and p[0] == "0": continue
            left = "".join(p); right = left[::-1]
            for mid in [[""], "0123456789"][d%2]:
                yield int(left + mid + right)
def a(n):
    for p in pals(startd=len(str(2**n-1))):
        if bin(p).count("1") == n:
            return p
print([a(n) for n in range(33)]) # Michael S. Branicky, Jun 02 2022

a(21)-a(32) from Michael S. Branicky, Jun 02 2022

cp's OEIS Frontend

A178065 Number of 1's in binary representation of n-th semiprime.

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