cp's OEIS Frontend

A256480 Smallest prime obtained by appending n to a nonzero number with identical digits or 0 if no such prime exists.

%I A256480 #16 May 22 2025 10:21:42
%S A256480 0,11,0,13,0,0,0,17,0,19,0,211,0,113,0,0,0,317,0,419,0,421,0,223,0,0,
%T A256480 0,127,0,229,0,131,0,233,0,0,0,137,0,139,0,241,0,443,0,0,0,347,0,149,
%U A256480 0,151,0,353,0,0,0,157,0,359,0,461,0,163,0,0,0,167,0,269
%N A256480 Smallest prime obtained by appending n to a nonzero number with identical digits or 0 if no such prime exists.
%C A256480 a(n) = 0 if n is even or a multiple of 5. Conjecture: all other terms are nonzero. Conjecture verified for n <= 10^7.
%C A256480 "Appending" means "on the right".
%H A256480 Chai Wah Wu, <a href="/A256480/b256480.txt">Table of n, a(n) for n = 0..10000</a>
%H A256480 Chai Wah Wu, <a href="http://arxiv.org/abs/1503.08883">On a conjecture regarding primality of numbers constructed from prepending and appending identical digits</a>, arXiv:1503.08883 [math.NT], 2015.
%o A256480 (Python)
%o A256480 from gmpy2 import digits, mpz, is_prime
%o A256480 def A256480(n,limit=2000):
%o A256480     sn = str(n)
%o A256480     if not (n % 2 and n % 5):
%o A256480         return 0
%o A256480     for i in range(1,limit+1):
%o A256480         for j in range(1,10):
%o A256480             si = digits(j,10)*i
%o A256480             p = mpz(si+sn)
%o A256480             if is_prime(p):
%o A256480                 return int(p)
%o A256480     else:
%o A256480         return 'search limit reached.'
%Y A256480 Cf. A090287, A256481.
%K A256480 nonn,base
%O A256480 0,2
%A A256480 _Chai Wah Wu_, Mar 31 2015