A244514 Numbers n such that the integers formed by all cyclic permutations of the decimal digits of n have the same prime divisors.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 486, 555, 648, 666, 777, 864, 888, 999, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111111, 222222, 242424, 333333, 424242, 444444

Offset

1,3

Comments

{a(n)} = {A010785} union {486, 648, 864, 242424, 424242, 484848, 486486, 648648, 848484, 864864,... } where A010785 are the repdigit numbers.

Links

Table of n, a(n) for n=1..55.

Example

486486 is in the sequence because the prime divisors of 486486, 864864 and 648648 are 2,3,7,11 and 13.

Maple

with(numtheory): T:=array(1..10):U:=array(1..10):
  for n from 11 to 10^6 do:
   c:=1:x:=convert(n, base, 10):n1:=nops(x):si:=factorset(n):
    for i from 1 to n1 do:T[i]:=x[n1-i+1]:od:
     for j from 1 to n1-1 do:
      for k from 1 to n1-1 do:
      U[k]:=T[k+1]:
      od:
     U[n1]:=T[1]:s:=sum('U[n1-p+1]*10^(p-1)', 'p'=1..n1):
     if factorset(s)=si
     then
     c:=c+1:
     else
     fi:
       for l from 1 to n1 do:
       T[l]:=U[l]:
       od:
        if c=n1
        then
        printf(`%d, `, n):
        else
        fi:
      od:
     od:

Crossrefs

Cf. A010785.

Sequence in context: A082937 A214019 A160818 * A082810 A344550 A010785

Adjacent sequences: A244511 A244512 A244513 * A244515 A244516 A244517

Keyword

nonn,base

Author

Michel Lagneau, Jun 29 2014

Extensions

Single-digit numbers added by N. J. A. Sloane, Jul 23 2014

Status

approved