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

1,2

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.

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 *)

Prog

(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

Crossrefs

Binary representation of A139102.

Subset of A118256.

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

Sequence in context: A215023 A071925 A346434 * A015482 A288582 A104486

Adjacent sequences: A139098 A139099 A139100 * A139102 A139103 A139104

Keyword

nonn,base

Author

Omar E. Pol, Apr 08 2008

Status

approved