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

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, 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, 2, 2, 2, 2, 2, 2, 7, 11, 3, 11, 11, 3, 11, 7, 3, 11, 2, 2, 2

Offset: 1

Author

Michel Lagneau, Apr 05 2014

Keywords

• nonn
• base
• easy

Comments

a(n) is the smallest prime divisor of A056524(n), or smallest prime divisor of the concatenation of a number n and reverse(n).

Examples

			a(10) = 7 because the concatenation of 10 and 01 is 1001 = 7*11*13 where 7 is the smallest divisor of 1001.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020639, A056524, A240453.

Programs

Maple

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:

Mathematica

d[n_]:=IntegerDigits[n];Table[FactorInteger[FromDigits[Join[x=d[n],Reverse[x]]]][[1,1]],{n,1,100}]
Table[FactorInteger[#][[1,1]]&/@Select[Range[10^n,10^(n+1)-1],PalindromeQ],{n,1,3,2}]//Flatten (* Harvey P. Dale, Jul 19 2021 *)

Python

from sympy import primefactors
def a(n): s = str(n); return min(primefactors(int(s + s[::-1])))
print([a(n) for n in range(1, 83)]) # Michael S. Branicky, Nov 02 2021

Formula

a(n) = A020639(A056524(n)).