A036229 Smallest n-digit prime containing only digits 1 or 2 or -1 if no such prime exists.

2, 11, 211, 2111, 12211, 111121, 1111211, 11221211, 111112121, 1111111121, 11111121121, 111111211111, 1111111121221, 11111111112221, 111111112111121, 1111111112122111, 11111111111112121, 111111111111112111, 1111111111111111111, 11111111111111212121

Offset: 1

Author

G. L. Honaker, Jr.

Keywords

• nonn
• base
• nice

Comments

It is conjectured that such a prime always exists.

a(2), a(19), a(23), etc. are the prime repunits (A004023). a(1000) = (10^n-1)/9 + 111011000010.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1000 (terms n=1..400 from Alois P. Heinz)
• Robert G. Wilson v, Comments and first 100 terms

Crossrefs

Cf. A036937, A068086.

Programs

Mathematica

Do[p = (10^n - 1)/9; k = 0; While[ ! PrimeQ[p], k++; p = FromDigits[ PadLeft[ IntegerDigits[ k, 2], n] + 1]]; Print[p], {n, 1, 20}]
Table[Min[Select[ FromDigits/@Tuples[{1,2},n],PrimeQ]],{n,20}] (* Harvey P. Dale, Feb 05 2014 *)

Python

from sympy import isprime
def A036229(n):
    k, r, m = (10**n-1)//9, 2**n-1, 0
    while m <= r:
        t = k+int(bin(m)[2:])
        if isprime(t):
            return t
        m += 1
    return -1 # Chai Wah Wu, Aug 18 2021

Extensions

Edited by N. J. A. Sloane and Robert G. Wilson v, May 03 2002

Escape clause added by Chai Wah Wu, Aug 18 2021