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A036229
Smallest n-digit prime containing only digits 1 or 2 or -1 if no such prime exists.
25
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
Sequence in context: A070256 A356523 A020450 * A104337 A283512 A214217
KEYWORD
nonn,base,nice
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