A055483 -id:A055483 - cp's OEIS frontend

A072032 a(n) = gcd(2^n, reverse(2^n)) = gcd(2^n, A004086(2^n)) = A055483(2^n).

2, 4, 8, 1, 1, 2, 1, 4, 1, 1, 2, 8, 2, 1, 1, 4, 1, 2, 1, 1, 2, 2, 2, 1, 1, 16, 1, 2, 1, 1, 4, 4, 2, 1, 1, 2, 1, 8, 1, 1, 8, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 8, 4, 1, 1, 1, 1, 1, 8, 1, 1, 16, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 8, 1, 1, 1, 1, 1, 1, 8, 1, 2, 2, 1, 1, 1, 1, 1, 1, 16, 1, 8, 1, 1

Offset: 1

Labos Elemer, Jun 07 2002

			n=12: a(12) = gcd(4096,6904) = 8.

Indranil Ghosh, Table of n, a(n) for n = 1..31180

Cf. A004086, A055483, A071686.

nd[x_, y_] := 10*x+y tn[x_] := Fold[nd, 0, x] red[x_] := Reverse[IntegerDigits[x]] Table[GCD[2^w, tn[red[2^w]]], {w, 1, 128}]

A371034 For n >= 1, a(n) = A004086(n) if A055483(n) = 1, otherwise a(n) = n / A055483(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 31, 41, 5, 61, 71, 2, 91, 10, 7, 1, 32, 4, 52, 13, 3, 14, 92, 10, 13, 23, 1, 43, 53, 4, 73, 83, 13, 10, 14, 7, 34, 1, 5, 23, 74, 4, 94, 10, 17, 25, 35, 6, 1, 65, 19, 85, 95, 10, 16, 31, 7, 32, 56, 1, 76, 34, 23, 10, 17, 8, 37, 47

Offset: 1

Ctibor O. Zizka, Mar 31 2024

Also a(n) = R(n) if (n, R(n)) are coprime, otherwise a(n) = n / GCD(n, R(n)), where R(n) is the digit reversal of n. a(n) = 1 for n from the union of A011557 and A002113 and A001232 and A008918.

			n = 13: A004086(13) = 31, A055483(13) = 1 thus a(13) = 31.
n = 15: A004086(15) = 51, A055483(15) = 3 thus a(15) = 15/3 = 5.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001232, A002113, A002275, A004086, A008918, A011557, A055483, A306273.

rev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
f:= proc(n) local r,g;
  r:= rev(n);
  g:= igcd(n,r);
  if g = 1 then r else n/g fi
end proc;
map(f, [$1..100]); # Robert Israel, Jul 09 2024

a[n_] := Module[{r = IntegerReverse[n], g}, g = GCD[n, r]; If[g == 1, r, n/g]]; Array[a, 100] (* Amiram Eldar, Mar 31 2024 *)

a(A011557(k)) = 1, k >= 0.
a(A002113(k)) = 1, k >= 2.
a(A001232(k)) = 1, k >= 1.
a(A008918(k)) = 1, k >= 1.

A071686 Smallest solution to gcd(x, Rev(x)) = 2^n.

Original entry on oeis.org

2, 4, 8, 2192, 21920, 291008, 610688, 2112256, 2131456, 2937856, 25329664, 230465536, 694018048, 2344321024, 4688642048, 2112421888, 65012891648, 650128916480, 4494196736, 63769149440, 637691494400, 23842827272192, 276298064723968, 420127895977984, 4897795987210240

Offset: 1

Labos Elemer, Jun 03 2002

Giovanni Resta, Table of n, a(n) for n = 1..32

Cf. A004086, A055483, A069554, A072005, A072021, A072050.

a[n_] := Block[{k = 2^n}, While[GCD[k, FromDigits@ Reverse@ IntegerDigits@ k] != 2^n, k += 2^n]; k]; Array[a, 17] (* Giovanni Resta, Nov 14 2019 *)

a(n) = A069554(2^n).

a(22)-a(25) from Giovanni Resta, Oct 29 2019

A072005 Smallest solution to gcd(k, reverse(k)) = 3^n.

Original entry on oeis.org

1, 3, 9, 2889, 2899999989, 4899999987, 19899999972, 29898999693, 49989958299, 49999917897, 99884394999, 372797889885, 1989767716659, 2678052898989, 17902896898419, 137530987695297, 189281899170567, 368055404997498, 14048104419899757, 437893473401621955, 218264275944702783

Offset: 0

Labos Elemer, Jun 04 2002

			n=4: 3^4 = 81, a(4) = 2899999989 = 3*3*3*3*35802469, reverse(a(4)) = 2*3*3*3*3*61111111; gcd = 81 = 3^n.

Sean A. Irvine, Table of n, a(n) for n = 0..25

Cf. A004086, A055483, A069554, A071686, A071686, A072021, A072050.

a(n) = A069554(3^n).

a(15)-a(20) from Giovanni Resta, Oct 30 2019

A072021 Smallest solution to gcd(x, reverse(x)) = 5^n.

Original entry on oeis.org

5, 5200, 521000, 5213750, 521875, 5218750, 52130234375, 5734841796875, 57869714843750, 526046650390625, 5265674365234375, 52187008544921875, 526515306396484375, 5213023309008789062500, 5213596736358642578125, 5260466086273193359375, 526041911745452880859375

Offset: 1

Labos Elemer, Jun 06 2002

			For n = 4, gcd(521875, 578125) = 3125 = 5^4.
For n = 8, a(8) = 5734841796875 = 5^9*2936239, reverse(a(8)) = 5786971484375 = 5^8*71*208657.

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..25

Cf. A004086, A055483, A069554, A071686, A072005, A072050, A072016-A072018.

a(n) = {my(k = 1); while (gcd(k, fromdigits(Vecrev(digits(k)))) != 5^n, k++); k;} \\ Michel Marcus, Jul 13 2018

a(n) = A069554(5^n).

a(9)-a(18) from Hiroaki Yamanouchi, Sep 10 2014

A071249 Numbers k such that gcd(k, R(k)) > 1, where R(k) (A004086) is the digit reversal of k.

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, 101, 102, 105, 108, 110, 111, 114, 117, 120, 121

Offset: 1

Amarnath Murthy, May 21 2002

Numbers k such that A055483(k) > 1. - Reinhard Zumkeller, Jun 18 2013

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

Cf. A004086, A055483, A226778 (complement).

a071249 n = a071249_list !! (n-1)
a071249_list = filter ((> 1) . a055483) [1..]
-- Reinhard Zumkeller, Jun 18 2013

Select[ Range[125], GCD[ #, FromDigits[ Reverse[ IntegerDigits[ # ]]]] > 1 & ]

Edited by Robert G. Wilson v, Jun 07 2002

Definition corrected by N. J. A. Sloane, Aug 27 2020 following a suggestion from José Hernández Santiago

A072016 Numbers k such that gcd(k, reverse(k)) = 27 = 3^3, where reverse(x) = A004086(x).

Original entry on oeis.org

2889, 3699, 3888, 3969, 4779, 4887, 5589, 5697, 5778, 5859, 5886, 5967, 6399, 6669, 6777, 6885, 6939, 7398, 7479, 7587, 7668, 7695, 7749, 7776, 7857, 7884, 7938, 7965, 8289, 8397, 8559, 8667, 8775, 8829, 8883, 8937, 9099, 9288, 9369, 9396, 9477, 9558, 9585

Offset: 1

Labos Elemer, Jun 05 2002

Solutions to gcd(k, reverse(k)) = 1,3,9 (lower powers of 3) are trivial (see A072005).

			2889 = 107*3*3*3, 9889 = 3*3*3*3*2*61.

Vincenzo Librandi, Table of n, a(n) for n = 1..1030

Cf. A004086, A055483, A069554, A071686, A072005.

[n: n in [1..10^4] | Gcd(n,Seqint(Reverse(Intseq(n)))) eq 27]; // Vincenzo Librandi, Jul 11 2018

Select[Range[10^4], GCD[#, FromDigits[Reverse[IntegerDigits[#]]]] == 27 &] (* Vincenzo Librandi, Jul 11 2018 *)

isok(n) = gcd(n, fromdigits(Vecrev(digits(n)))) == 27; \\ Michel Marcus, Jul 11 2018

A072050 Smallest solution to GCD(x,A004086(x))=7^n.

Original entry on oeis.org

7, 18718, 343, 125204947, 231012215, 11298657013, 211066659013, 117088913464607, 2846847905744815, 108244538579770418, 2080795357577501075, 18312871825384462928, 26268977180287044053417, 1734582041294009627423816

Offset: 1

Labos Elemer, Jun 10 2002

Cf. A004086, A055483, A069554, A071686, A072005, A072021.

Mathematica
```
(* See A071686. *)
```

a(n) = A069554(7^n).

a(8)-a(9) from Max Alekseyev, Jun 17 2011

a(10)-a(14) from Giovanni Resta, Oct 30 2019

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

A256756 a(n) = bitwise XOR of n and the reverse of n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 25, 18, 39, 60, 45, 86, 67, 72, 22, 25, 0, 55, 50, 45, 36, 83, 78, 65, 29, 18, 55, 0, 9, 22, 27, 108, 117, 122, 44, 39, 50, 9, 0, 27, 110, 101, 100, 111, 55, 60, 45, 22, 27, 0, 121, 114, 111, 100, 58, 45, 36, 27, 110, 121

Offset: 0

Alois P. Heinz, Apr 09 2015

Alois P. Heinz, Table of n, a(n) for n = 0..10000
Wikipedia, Bitwise operation

Cf. A003987, A004086, A055483, A056964, A056965, A061205, A068634, A175919, A256754, A256755.

a:= n-> Bits[Xor](n, (s-> parse(cat(s[-i]$i=1..length(s))))(""||n)):
seq(a(n), n=0..80);

Table[BitXor[n,FromDigits[Reverse[IntegerDigits[n]]]],{n,0,65}] (* Ivan N. Ianakiev, Apr 10 2015 *)

a(n) = bitxor(n, subst(Polrev(digits(n)), x, 10)); \\ Michel Marcus, Apr 10 2015

a(n) = A003987(n, A004086(n)).

cp's OEIS Frontend

A072032 a(n) = gcd(2^n, reverse(2^n)) = gcd(2^n, A004086(2^n)) = A055483(2^n).

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A371034 For n >= 1, a(n) = A004086(n) if A055483(n) = 1, otherwise a(n) = n / A055483(n).

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A071686 Smallest solution to gcd(x, Rev(x)) = 2^n.

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A072005 Smallest solution to gcd(k, reverse(k)) = 3^n.

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A072021 Smallest solution to gcd(x, reverse(x)) = 5^n.

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PARI

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A071249 Numbers k such that gcd(k, R(k)) > 1, where R(k) (A004086) is the digit reversal of k.

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A072016 Numbers k such that gcd(k, reverse(k)) = 27 = 3^3, where reverse(x) = A004086(x).

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Magma

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A072050 Smallest solution to GCD(x,A004086(x))=7^n.

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