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A256481 Smallest prime obtained by appending a number with identical digits to n or 0 if no such prime exists.

%I A256481 #11 May 22 2025 10:21:42
%S A256481 2,11,23,31,41,53,61,71,83,97,101,113,127,131,149,151,163,173,181,191,
%T A256481 2011,211,223,233,241,251,263,271,281,293,307,311,3299,331,347,353,
%U A256481 367,373,383,397,401,419,421,431,443,457,461,479,487,491,503,511111,521,5333
%N A256481 Smallest prime obtained by appending a number with identical digits to n or 0 if no such prime exists.
%C A256481 For n <= 15392, a(n) = 0 if and only if n = 6930. Conjecture: if a(n) = 0, then n is divisible by 3. Conjecture verified for n <= 10^6.  a(n) = 0 for n = 6930, 50358, 56574, 72975.
%H A256481 Chai Wah Wu, <a href="/A256481/b256481.txt">Table of n, a(n) for n = 0..6068</a>
%H A256481 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 A256481 (Python)
%o A256481 from gmpy2 import mpz, digits, is_prime
%o A256481 def A256481(n,limit=2000):
%o A256481     if n in (6930,50358,56574,72975):
%o A256481         return 0
%o A256481     if n == 0:
%o A256481         return 2
%o A256481     sn = str(n)
%o A256481     for i in range(1,limit+1):
%o A256481         for j in range(1,10,2):
%o A256481             si = digits(j,10)*i
%o A256481             p = mpz(sn+si)
%o A256481             if is_prime(p):
%o A256481                 return int(p)
%o A256481     else:
%o A256481         return 'search limit reached.'
%Y A256481 Cf. A090287, A256480, A030665.
%K A256481 nonn,base
%O A256481 0,1
%A A256481 _Chai Wah Wu_, Mar 31 2015