A387356 Numbers whose set of cyclic permutations has GCD = 1.

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, 101, 103, 104, 106, 107, 109, 110, 112, 113, 115, 116, 118, 119, 121, 122, 124, 125, 127, 128, 130

Offset

1,2

Comments

First differs from A226778 at n = 44: a(44) = 101 while A226778(44) = 103.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Example

1234 is a term because GCD(1234,2341,3412,4123) = 1.

Maple

filter:= proc(n) local m, x, i, g;
  m:= ilog10(n);
  x:= n; g:= n;
  for i from 1 to m do
    x:= floor(x/10) + (x mod 10)*10^m;
    g:= igcd(g, x);
    if g = 1 then return true fi;
  od;
  false
end proc:
filter(1):= true:
select(filter, [$1..130]); # Robert Israel, Sep 02 2025

Mathematica

A387356Q[k_] := GCD @@ Map[FromDigits, NestList[RotateLeft, #, Length[#] - 1] & [IntegerDigits[k]]] == 1;
Select[Range[200], A387356Q]

Crossrefs

Complement of A084433. Subset of A001651.

Cf. A226778, A287513, A339076.

Sequence in context: A070837 A188643 A087140 * A226778 A061837 A256477

Adjacent sequences: A387353 A387354 A387355 * A387357 A387358 A387359

Keyword

nonn,base

Author

Paolo Xausa, Aug 27 2025

Status

approved