A383919 - OEIS

A383919

Primes made up of 0's and seven 1's only.

11110111, 11111101, 101101111, 101111011, 110111011, 111010111, 1001110111, 1010011111, 1011110011, 1100101111, 1101010111, 1101110011, 1110011101, 1110110011, 1111100101, 1111110001, 10010110111, 10011101011, 10011110101, 10100111101, 10111001011, 10111110001, 11001011101

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OFFSET

1,1

COMMENTS

Expression of the primes that are 0-successors of the preprime 1111111 (= 239*4649); they constitute the infinite set of secondary primes with seven 1's and zeros denoted {1111111} (Definitions 1, 2, 3, 4 of Clerc).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..12277

René-Louis Clerc, Nombres premiers primaires et nombres premiers secondaires, zenodo.19022321, 2026.

PROG

(PARI) list(M) = for(i=3, M, for(j=2, i-1, for(k=1, j-1, for(r=1, k-1, for(l=1, r-1, for(m=1, l-1, my(p=10^i+10^j+10^k+10^r+10^l+10^m+1); isprime(p) && print1(p, ", ")))))))

(Python)

from itertools import count, islice

from sympy import isprime

def A383919_gen(): # generator of terms

for a in count(6):

for b in range(5, a):

for c in range(4, b):

for d in range(3, c):

for e in range(2, d):

for f in range(1, e):

if isprime(p:=10**a+10**b+10**c+10**d+10**e+10**f|1):

yield(p)