A181775 Numbers k such that the decimal digits of k*(k+1) are a permutation of those of k*(k-1).

153, 729, 900, 3420, 4221, 4500, 4779, 4851, 5400, 9153, 13500, 13779, 22500, 24498, 31500, 36927, 40500, 46647, 49221, 49779, 50202, 55152, 61353, 68994, 69894, 77499, 80064, 82872, 83637, 84249, 90495, 102402

Offset

1,1

Comments

All terms are divisible by 9. - Robert Israel, May 12 2020

Links

Robert Israel, Table of n, a(n) for n = 1..2500

Example

729 is in the sequence because 729*730 = 532170 and 729*728 = 530712.

Maple

filter:= n -> sort(convert(n*(n+1), base, 10))=sort(convert(n*(n-1), base, 10)):
select(filter, [seq(i, i=9..200000, 9)]); # Robert Israel, May 11 2020

Mathematica

okQ[n_]:=Module[{idn=IntegerDigits[n^2+n]}, Sort[idn]==Sort[IntegerDigits[n^2-n]]]; Select[Range[100000], okQ]

Prog

(PARI) isok(k) = vecsort(digits(k*(k+1))) == vecsort(digits(k*(k-1))); \\ Michel Marcus, May 12 2020

Crossrefs

Cf. A334798.

Sequence in context: A325376 A256740 A199851 * A193249 A050209 A109142

Adjacent sequences: A181772 A181773 A181774 * A181776 A181777 A181778

Keyword

nonn,base

Author

Michel Lagneau

Status

approved