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%I #55 Jun 02 2021 04:03:51
%S 142857,1429857,14299857,142999857,1429999857,14299999857,
%T 142857142857,142999999857,1428571429857,1429857142857,1429999999857,
%U 14285714299857,14298571429857,14299857142857,14299999999857,137428291864557,137464282918557,142829186455737
%N 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.
%C All terms are divisible by 9.
%C a(1) = 143*999 = 1287*111;
%C a(2) = 143*9999 = 1287*1111;
%C a(7) = 143*999000999 = 1287*111000111; etc.
%C 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
%e 142857, 1429857, and 14299857 are in the sequence:
%e .
%e k 2*k 3*k 4*k 5*k 6*k
%e -------- -------- -------- -------- -------- --------
%e 142857 285714 428571 571428 714285 857142
%e 1429857 2859714 4289571 5719428 7149285 8579142
%e 14299857 28599714 42899571 57199428 71499285 85799142
%o (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
%Y Cf. A023086, A245682, A323711.
%K nonn,base
%O 1,1
%A _Bhupendra Kumar Singh_, May 19 2021
%E Data corrected by _David A. Corneth_, May 22 2021