|
| |
|
|
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
|
Cf. A036937, A068086.
Sequence in context: A188203 A070256 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
|
| |
|
|
