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

1,1

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).

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A020639, A056524, A240453.

Sequence in context: A070277 A109864 A231433 * A099756 A088277 A089744

Adjacent sequences: A240451 A240452 A240453 * A240455 A240456 A240457

Keyword

nonn,base,easy

Author

Michel Lagneau, Apr 05 2014

Status

approved