A108848 Palindromic primes in which all internal digits are 9.

191, 797, 19991, 79997, 199999991, 79999999999999999999999999997, 19999999999999999999999999999999999999991, 199999999999999999999999999999999999999999999999999999999999999999999999999999999999991

Offset: 1

Author

Cino Hilliard, Jul 11 2005

Keywords

• easy
• nonn
• base

Comments

Obviously, 1 and 7 are the only possible outer digits for repeating inner digit 9.

Terms a(14), a(15), and a(16) have respectively 1213, 1285, and 1461 digits. - Harvey P. Dale, Dec 11 2019

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..13

Crossrefs

Similar sequences for digit d: A108845 (d=1), A108846 (d=2), A108841 (d=4), A108842 (d=5), A108843 (d=6), A108844 (d=7), A108847 (d=8), A108848 (d=9).

Programs

Mathematica

Select[Flatten[Table[FromDigits[PadRight[{k},n,9]]*10+k,{n,2,200},{k,{1,7}}]],PrimeQ] (* Harvey P. Dale, Dec 11 2019 *)

PARI

n10np9(n,d) = { local(x,y,k); for(x=1,n, for(k=1,9, y=10^(x+1)*k+(10^x-1)*10+k; if(isprime(y),print1(y",")) ) ) }

Python

from sympy import isprime
from itertools import count, islice
def agen(): yield from (t for i in count(1) for f in "17" if isprime(t:=int(f + "9"*i + f)))
print(list(islice(agen(), 13))) # Michael S. Branicky, Jan 27 2023

Extensions

Name changed by Arkadiusz Wesolowski, Sep 07 2011

More terms from Harvey P. Dale, Dec 11 2019