login
A370069
Lexicographically earliest sequence of distinct integers such that the concatenated binary expansions of the terms is A010051.
1
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
1,3
COMMENTS
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).
LINKS
EXAMPLE
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
MATHEMATICA
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
PROG
(Python)
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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
STATUS
approved