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A256048 Smallest palindromic prime by adding at least one digit to both the left and right of n.

%I A256048 #15 Jul 23 2025 15:12:52
%S A256048 101,313,727,131,11411,151,10601,373,181,191,30103,1114111,1120211,
%T A256048 11311,11411,31513,1160611,1117111,18181,71917,30203,1120211,72227,
%U A256048 32323,12421,1250521,36263,12721,12821,39293,10301,11311,32323,13331,14341,33533,16361,77377
%N A256048 Smallest palindromic prime by adding at least one digit to both the left and right of n.
%H A256048 Chai Wah Wu, <a href="/A256048/b256048.txt">Table of n, a(n) for n = 0..10000</a>
%o A256048 (Python)
%o A256048 from __future__ import division
%o A256048 from sympy import isprime
%o A256048 def palgenrange2(m,l): # generator of odd-length palindromes of length at least m and at most 2*l
%o A256048     if m == 1:
%o A256048         yield 0
%o A256048     for x in range(m//2+1,l+1):
%o A256048         n = 10**(x-1)
%o A256048         for y in range(n,n*10):
%o A256048             s = str(y)
%o A256048             yield int(s+s[-2::-1])
%o A256048 def A256048(n):
%o A256048     sn = str(n)
%o A256048     for p in palgenrange2(len(sn)+2,len(sn)+20):
%o A256048         if sn in str(p)[1:-1] and isprime(p):
%o A256048             break
%o A256048     else:
%o A256048         return 'search limit reached'
%o A256048     return p # _Chai Wah Wu_, Mar 22 2015
%Y A256048 Cf. A090287
%K A256048 nonn,base
%O A256048 0,1
%A A256048 _Felix Fröhlich_, Mar 10 2015
%E A256048 a(10), a(12), a(16), a(18) corrected by _Chai Wah Wu_, Mar 22 2015