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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 (list; graph; refs; listen; history; text; internal format)
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
AUTHOR
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

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Last modified April 20 00:58 EDT 2024. Contains 371798 sequences. (Running on oeis4.)