login
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.
0
142857, 1429857, 14299857, 142999857, 1429999857, 14299999857, 142857142857, 142999999857, 1428571429857, 1429857142857, 1429999999857, 14285714299857, 14298571429857, 14299857142857, 14299999999857, 137428291864557, 137464282918557, 142829186455737
OFFSET
1,1
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
EXAMPLE
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
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
Data corrected by David A. Corneth, May 22 2021
STATUS
approved