Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #20 May 12 2020 10:59:32
%S 153,729,900,3420,4221,4500,4779,4851,5400,9153,13500,13779,22500,
%T 24498,31500,36927,40500,46647,49221,49779,50202,55152,61353,68994,
%U 69894,77499,80064,82872,83637,84249,90495,102402
%N Numbers k such that the decimal digits of k*(k+1) are a permutation of those of k*(k-1).
%C All terms are divisible by 9. - _Robert Israel_, May 12 2020
%H Robert Israel, <a href="/A181775/b181775.txt">Table of n, a(n) for n = 1..2500</a>
%e 729 is in the sequence because 729*730 = 532170 and 729*728 = 530712.
%p filter:= n -> sort(convert(n*(n+1),base,10))=sort(convert(n*(n-1),base,10)):
%p select(filter, [seq(i,i=9..200000,9)]); # _Robert Israel_, May 11 2020
%t okQ[n_]:=Module[{idn=IntegerDigits[n^2+n]},Sort[idn]==Sort[IntegerDigits[n^2-n]]];Select[Range[100000],okQ]
%o (PARI) isok(k) = vecsort(digits(k*(k+1))) == vecsort(digits(k*(k-1))); \\ _Michel Marcus_, May 12 2020
%Y Cf. A334798.
%K nonn,base
%O 1,1
%A _Michel Lagneau_