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%I #26 Mar 27 2026 04:30:13
%S 11110111,11111101,101101111,101111011,110111011,111010111,1001110111,
%T 1010011111,1011110011,1100101111,1101010111,1101110011,1110011101,
%U 1110110011,1111100101,1111110001,10010110111,10011101011,10011110101,10100111101,10111001011,10111110001,11001011101
%N Primes made up of 0's and seven 1's only.
%C 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).
%H Alois P. Heinz, <a href="/A383919/b383919.txt">Table of n, a(n) for n = 1..12277</a>
%H René-Louis Clerc, <a href="https://zenodo.org/records/19022321">Nombres premiers primaires et nombres premiers secondaires</a>, zenodo.19022321, 2026.
%o (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, ", ")))))))
%o (Python)
%o from itertools import count, islice
%o from sympy import isprime
%o def A383919_gen(): # generator of terms
%o for a in count(6):
%o for b in range(5,a):
%o for c in range(4,b):
%o for d in range(3,c):
%o for e in range(2,d):
%o for f in range(1,e):
%o if isprime(p:=10**a+10**b+10**c+10**d+10**e+10**f|1):
%o yield(p)
%o A383919_list = list(islice(A383919_gen(),23)) # _Chai Wah Wu_, May 28 2025
%Y Intersection of A020449 and A062337.
%Y Cf. A157711, A038447, A020449.
%K nonn,base
%O 1,1
%A _René-Louis Clerc_, May 15 2025