A055483 a(n) is the GCD of n and the reverse of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 3, 1, 1, 3, 1, 1, 9, 1, 2, 3, 22, 1, 6, 1, 2, 9, 2, 1, 3, 1, 1, 33, 1, 1, 9, 1, 1, 3, 4, 1, 6, 1, 44, 9, 2, 1, 12, 1, 5, 3, 1, 1, 9, 55, 1, 3, 1, 1, 6, 1, 2, 9, 2, 1, 66, 1, 2, 3, 7, 1, 9, 1, 1, 3, 1, 77, 3, 1, 8, 9, 2, 1, 12, 1, 2, 3, 88, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 99, 1, 101, 3, 1, 1, 3, 1, 1, 9, 1, 11, 111

Offset: 1

Author

Erich Friedman, Jun 27 2000

Keywords

• base
• easy
• nonn
• nice

Comments

a(A226778(n)) = 1; a(A071249(n)) > 1. - Reinhard Zumkeller, Jun 18 2013

a(n) = n iff n >= 1 is a palindrome (n is in A002113). - Felix Fröhlich, Oct 28 2014

Examples

			a(12) = 3 since gcd(12, 21) = 3.
a(13) = 1 since 13 and 31 are coprime.
a(101) = gcd(101, 101) = 101.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..50000 (first 1000 terms from T. D. Noe)

Crossrefs

Different from A069652, first differs at a(101), since gcd(101, 110) = 1.

Cf. A002113, A004086, A071249, A226778.

Programs

Haskell

a055483 n = gcd n $ a004086 n  -- Reinhard Zumkeller, Jun 18 2013

Magma

[Gcd(n, Seqint(Reverse(Intseq(n)))): n in [1..100]]; // Vincenzo Librandi, Oct 29 2014

Mathematica

gcn[n_] := GCD[n, IntegerReverse[n]]; Array[gcn, 120] (* Harvey P. Dale, Jan 23 2012 *)

PARI

a004086(n)=eval(concat(Vecrev(Str(n))))
a(n)=gcd(n, a004086(n)) \\ Felix Fröhlich, Oct 28 2014

Python

from math import gcd
def a(n): return gcd(n, int(str(n)[::-1]))
print([a(n) for n in range(1, 112)]) # Michael S. Branicky, Aug 31 2021

Scala

def reverseDigits(n: Int): Int = Integer.parseInt(n.toString.reverse)
def euclGCD(a: Int, b: Int): Int = b match { case 0 => a; case n => Math.abs(euclGCD(b, a % b)) }
(1 to 120).map(n => euclGCD(n, reverseDigits(n))) // Alonso del Arte, Aug 31 2021

Formula

a(n) = gcd(n, A004086(n)). - Felix Fröhlich, Oct 28 2014

3 | a(n) if 3 | n and 9 | a(n) if 9 | n. - Alonso del Arte, Aug 31 2021

Extensions

Edited by Robert G. Wilson v, Apr 10 2002