A344436 Numbers k such that k, 2*k, 3*k, 4*k, 5*k and 6*k are anagrams and no digit of k is zero.

142857, 1429857, 14299857, 142999857, 1429999857, 14299999857, 142857142857, 142999999857, 1428571429857, 1429857142857, 1429999999857, 14285714299857, 14298571429857, 14299857142857, 14299999999857, 137428291864557, 137464282918557, 142829186455737

Offset: 1

Author

Bhupendra Kumar Singh, May 19 2021

Keywords

• nonn
• base

Comments

All terms are divisible by 9.

a(1) = 143*999 = 1287*111;

a(2) = 143*9999 = 1287*1111;

a(7) = 143*999000999 = 1287*111000111; etc.

a(n) = k is odd. Proof: If k is even then 5*k ends in 0, which is forbidden by definition. - David A. Corneth, May 22 2021

Examples

			142857, 1429857, and 14299857 are in the sequence:
.
      k        2*k       3*k       4*k       5*k       6*k
  --------  --------  --------  --------  --------  --------
    142857    285714    428571    571428    714285    857142
   1429857   2859714   4289571   5719428   7149285   8579142
  14299857  28599714  42899571  57199428  71499285  85799142
		

Crossrefs

Cf. A023086, A245682, A323711.

Programs

PARI

isok(k) = {my(d = vecsort(digits(k))); vecmin(d) && (d==vecsort(digits(2*k))) && (d==vecsort(digits(3*k))) && (d==vecsort(digits(4*k))) && (d==vecsort(digits(5*k))) && (d==vecsort(digits(6*k)));} \\ Michel Marcus, Jun 01 2021

Extensions

Data corrected by David A. Corneth, May 22 2021