cp's OEIS Frontend

A068160 Smallest prime beginning and ending in exactly n 1's and containing at least one digit != 1.

%I A068160 #18 Oct 02 2024 12:18:36
%S A068160 2,101,11311,1114111,111181111,111110611111,1111118111111,
%T A068160 111111151111111,111111110911111111,11111111128111111111,
%U A068160 111111111161111111111,111111111110911111111111,11111111111104111111111111,1111111111111031111111111111,11111111111111611111111111111,11111111111111173111111111111111
%N A068160 Smallest prime beginning and ending in exactly n 1's and containing at least one digit != 1.
%C A068160 a(499) has 1001 digits. - _Michael S. Branicky_, Oct 02 2024
%H A068160 Michael S. Branicky, <a href="/A068160/b068160.txt">Table of n, a(n) for n = 0..498</a>
%e A068160 a(2) = 11311 is a prime that starts with 11 and ends in 11 (two 1's).
%o A068160 (Python)
%o A068160 from gmpy2 import is_prime
%o A068160 def a(n):
%o A068160     suffix, d = (10**n-1)//9, 2*n+1
%o A068160     while True:
%o A068160         prefix = 10**(d-n)*suffix
%o A068160         for mid in range(0, 10**(d-n), 10**n):
%o A068160             s = str(mid//10**n)
%o A068160             if s[0] == "1" or s[-1] == "1": continue
%o A068160             t = prefix + mid + suffix
%o A068160             if is_prime(t): return t
%o A068160         d += 1
%o A068160 print([a(n) for n in range(16)]) # _Michael S. Branicky_, Oct 02 2024
%Y A068160 Cf. A366416.
%K A068160 nonn,base
%O A068160 0,1
%A A068160 _Amarnath Murthy_, Feb 24 2002
%E A068160 Corrected and extended by _Sascha Kurz_, Jan 03 2003
%E A068160 More precise name and more terms from _Hugo Pfoertner_, Oct 11 2023
%E A068160 a(0) = 2 inserted by _Michael S. Branicky_, Oct 02 2024