A068685 Primes which are a sandwich of numbers using at most one digit between two 1's.

11, 101, 131, 151, 181, 191, 13331, 15551, 16661, 19991, 1333331, 1444441, 1777771, 188888881, 199999991, 1666666666661, 188888888888881, 16666666666666661, 1111111111111111111, 1666666666666666661, 155555555555555555551, 11111111111111111111111

Offset: 1

Author

Amarnath Murthy, Mar 02 2002

Keywords

• base
• nonn

Comments

a(47) has 1003 digits. - Michael S. Branicky, Jan 28 2023

Examples

			11 is a member sandwiching nothing between two 1's. 13331 is a sandwich using 333.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..46

Crossrefs

Cf. A068683.

Programs

Mathematica

Select[Union[Flatten[Table[FromDigits[Join[{1},PadRight[{},n,i],{1}]], {n,0,20},{i,0,9}]]],PrimeQ] (* Harvey P. Dale, Mar 29 2012 *)

Python

from sympy import isprime
from itertools import count, islice
def agen(): yield 11; yield from (t for i in count(1) for m in "0123456789" if isprime(t:=int("1" + m*i + "1")))
print(list(islice(agen(), 30))) # Michael S. Branicky, Jan 28 2023

Extensions

More terms from Sascha Kurz, Mar 17 2002

a(21) and beyond from Michael S. Branicky, Jan 28 2023