A139101 Numbers that show the distribution of prime numbers up to the n-th prime minus 1, using "0" for primes and "1" for nonprime numbers.

1, 10, 1001, 100101, 1001010111, 100101011101, 1001010111010111, 100101011101011101, 1001010111010111010111, 1001010111010111010111011111, 100101011101011101011101111101, 100101011101011101011101111101011111, 1001010111010111010111011111010111110111

Offset: 1

Author

Omar E. Pol, Apr 08 2008

Keywords

• nonn
• base

Comments

a(n) has A000040(n)-1 digits, n-1 digits "0" and A000040(n)-n digits "1".

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..168
• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Crossrefs

Binary representation of A139102.

Subset of A118256.

Cf. A000040, A018252, A139103, A139104, A139119, A139120, A139122.

Programs

Mathematica

Table[ sum = 0; For[i = 1, i <= Prime[n] - 1 , i++, sum = sum*2;
If[! PrimeQ[i], sum++]]; IntegerString[sum, 2], {n, 1, 13}] (* Robert Price, Apr 03 2019 *)

PARI

a(n) = fromdigits(vector(prime(n)-1, k, !isprime(k)), 10); \\ Michel Marcus, Apr 04 2019

Python

from sympy import isprime, prime
def a(n): return int("".join(str(1-isprime(i)) for i in range(1, prime(n))))
print([a(n) for n in range(1, 14)]) # Michael S. Branicky, Jan 10 2022

Python

# faster version for initial segment of sequence
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    an = 0
    for k in count(1):
        an = 10 * an + int(not isprime(k))
        if isprime(k+1):
            yield an
print(list(islice(agen(), 13))) # Michael S. Branicky, Jan 10 2022