A022340 -id:A022340 - cp's OEIS frontend

A370069 Lexicographically earliest sequence of distinct integers such that the concatenated binary expansions of the terms is A010051.

0, 1, 2, 40, 162, 8, 32, 160, 34, 544, 130, 520, 2568, 8320, 552, 663552, 2178, 512, 10272, 34848, 2560, 665600, 2048, 35360, 163872, 2080, 10274, 8396800, 9052160, 33280, 2592, 128, 33288, 133128, 131584, 10242, 33312, 2056, 165888, 526464, 2230272, 655360, 2129952, 8352, 32800, 534560, 141312, 2050, 139394, 32776

Offset: 1

Giorgos Kalogeropoulos, Feb 08 2024

If we take the binary expansion of each term and concatenate these bits to a sequence, we get the sequence of the characteristic function of primes (A010051).

For n > 2 every term is an even Fibbinary number (A022340).

			terms   0,   1,    2,         40,             162,            8,          32
binary {0}, {1}, {1,0}, {1,0,1,0,0,0}, {1,0,1,0,0,0,1,0}, {1,0,0,0}, {1,0,0,0,0,0}
A010051 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf A010051, A022340, A003714, A030190, A139102.

n=49; lst={0};p=2;c=Boole[PrimeQ@Range[n^2]]; Do[k=1;While[MemberQ[lst,ne=FromDigits[c[[p;;(pn=NextPrime[p,k])-1]],2]],k++]; AppendTo[lst,ne];p=pn,{i,n}];lst

from sympy import nextprime
from itertools import islice
def agen(): # generator of terms
    yield 0
    p, nextp, aset = 2, 3, {0}
    while True:
        an = 0
        while an in aset:
            an = (an<<(nextp-p)) + (1<<(nextp-p-1))
            p, nextp = nextp, nextprime(nextp)
        yield an
        aset.add(an)
print(list(islice(agen(), 50))) # Michael S. Branicky, Feb 08 2024

cp's OEIS Frontend

A370069 Lexicographically earliest sequence of distinct integers such that the concatenated binary expansions of the terms is A010051.

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