A071249 -id:A071249 - cp's OEIS frontend

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

Erich Friedman, Jun 27 2000

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

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

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

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

Cf. A002113, A004086, A071249, A226778.

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

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

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

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

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

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

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

Edited by Robert G. Wilson v, Apr 10 2002

A226778 Numbers having no common divisor > 1 with their reversal in decimal representation (see A043537).

Original entry on oeis.org

1, 10, 13, 14, 16, 17, 19, 23, 25, 29, 31, 32, 34, 35, 37, 38, 41, 43, 47, 49, 52, 53, 56, 58, 59, 61, 65, 67, 71, 73, 74, 76, 79, 83, 85, 89, 91, 92, 94, 95, 97, 98, 100, 103, 104, 106, 107, 109, 112, 113, 115, 116, 118, 119, 122, 124, 125, 127, 128, 130

Offset: 1

Reinhard Zumkeller, Jun 18 2013

A055483(a(n)) = 1.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A043537, A055483, A071249 (complement).

a226778 n = a226778_list !! (n-1)
a226778_list = filter ((== 1) . a055483) [1..]

Select[Range[130], GCD[#, FromDigits[Reverse[IntegerDigits[#]]]] == 1 &] (* Jayanta Basu, Jul 24 2013 *)
Select[Range[150],Intersection[Divisors[#],Divisors[IntegerReverse[#]]] == {1}&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 07 2020 *)

isok(n) = gcd(n, subst(Pol(Vecrev(digits(n))), x, 10)) == 1; \\ Michel Marcus, Jul 02 2015

is(n)=gcd(fromdigits(Vecrev(digits(n))), n)==1 \\ Charles R Greathouse IV, Aug 25 2016

A084434 Numbers whose digit permutations have GCD > 1.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 18, 20, 21, 22, 24, 26, 27, 28, 30, 33, 36, 39, 40, 42, 44, 45, 46, 48, 50, 51, 54, 55, 57, 60, 62, 63, 64, 66, 68, 69, 70, 72, 75, 77, 78, 80, 81, 82, 84, 86, 87, 88, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132

Offset: 1

Amarnath Murthy, Jun 02 2003

Numbers k such that there is a number d>1 which divides every number that can be obtained by permuting the digits of k. - N. J. A. Sloane, Aug 27 2020

Theorem. The sequence consists of: (1) A008585 (multiples of 3), (2) A014263 (numbers with all digits even), (3) A014181 (numbers with all digits equal), (4) numbers with all digits 5 or 0, (5) numbers with all digits 7 or 0, (6) numbers with 6k digits, all of which are 1 or 8, and (7) numbers with 6k digits, all of which are 2 or 9. - David Wasserman, May 07 2004

			72 is in the sequence because 72 and 27 are both divisible by 9.

Cf. A008585, A014181, A014263, A071249.

Subsequence of A084433 which contains for example 592 which is not in here.

Select[Range[0, 150], GCD @@ FromDigits /@ Permutations[IntegerDigits[#]] > 1 &]  (* Harvey P. Dale, Jan 12 2011 *)

More terms from David Wasserman, May 07 2004
Initial zero removed, Harvey P. Dale, Jan 14 2011
Entry revised by N. J. A. Sloane, Aug 27 2020

cp's OEIS Frontend

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

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A226778 Numbers having no common divisor > 1 with their reversal in decimal representation (see A043537).

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Haskell

Mathematica

PARI

PARI

A084434 Numbers whose digit permutations have GCD > 1.

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Author

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Programs

Mathematica

Extensions