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A240454 Smallest prime divisors of the palindromes with an even number of digits.

%I A240454 #19 Nov 02 2021 09:52:16
%S A240454 11,2,3,2,5,2,7,2,3,7,11,3,11,11,3,11,7,3,11,2,2,2,2,2,2,2,2,2,2,3,11,
%T A240454 11,3,11,11,3,7,11,3,2,2,2,2,2,2,2,2,2,2,5,3,5,5,3,5,5,3,5,5,2,2,2,2,
%U A240454 2,2,2,2,2,2,7,11,3,11,11,3,11,7,3,11,2,2,2
%N A240454 Smallest prime divisors of the palindromes with an even number of digits.
%C A240454 a(n) is the smallest prime divisor of A056524(n), or smallest prime divisor of the concatenation of a number n and reverse(n).
%H A240454 Michel Lagneau, <a href="/A240454/b240454.txt">Table of n, a(n) for n = 1..10000</a>
%F A240454 a(n) = A020639(A056524(n)).
%e A240454 a(10) = 7 because the concatenation of 10 and 01 is 1001 = 7*11*13 where 7 is the smallest divisor of 1001.
%p A240454 with(numtheory):for n from 1 to 100 do:x:=convert(n,base,10):n1:=nops(x): s:=sum('x[i]*10^(n1-i)', 'i'=1..n1):y:=n*10^n1+s:z:=factorset(y):n2:=nops(z):d:=z[1]:printf(`%d, `,d):od:
%t A240454 d[n_]:=IntegerDigits[n];Table[FactorInteger[FromDigits[Join[x=d[n],Reverse[x]]]][[1,1]],{n,1,100}]
%t A240454 Table[FactorInteger[#][[1,1]]&/@Select[Range[10^n,10^(n+1)-1],PalindromeQ],{n,1,3,2}]//Flatten (* _Harvey P. Dale_, Jul 19 2021 *)
%o A240454 (Python)
%o A240454 from sympy import primefactors
%o A240454 def a(n): s = str(n); return min(primefactors(int(s + s[::-1])))
%o A240454 print([a(n) for n in range(1, 83)]) # _Michael S. Branicky_, Nov 02 2021
%Y A240454 Cf. A020639, A056524, A240453.
%K A240454 nonn,base,easy
%O A240454 1,1
%A A240454 _Michel Lagneau_, Apr 05 2014