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

1,1

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

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 *)

Prog

(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

Crossrefs

Cf. A036937, A068086.

Sequence in context: A070256 A356523 A020450 * A104337 A283512 A214217

Adjacent sequences: A036226 A036227 A036228 * A036230 A036231 A036232

Keyword

nonn,base,nice

Author

G. L. Honaker, Jr.

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

Status

approved