A151946 a(1) = 8127; thereafter a(n) = (a(n-1) with digits sorted into descending order) - (a(n-1) with digits sorted into ascending order) (see the Kaprekar map, A151949).

8127, 7443, 3996, 6264, 4176, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174

Offset

1,1

Comments

Similar in spirit to the RATS (Reverse, Add Then Sort) sequences.

Converges to the fixed point 6174. For the list of fixed points see A099009.

The initial value 1001 is the smallest number that converges to 6174 - see A151967.

Links

Table of n, a(n) for n=1..39.

John Tierney, "TierneyLab" column, New York Times, Section C, Aug 18 2009

Index entries for the Kaprekar map

Index entries for periodic sequences.

Index entries for RATS sequences

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

a(n) = 6174 for n > 5. - Charles R Greathouse IV, May 30 2026

Mathematica

NestList[FromDigits[ReverseSort[#]] - FromDigits[Sort[#]] & [IntegerDigits[#]] &, 8127, 49] (* or *)
PadRight[{8127, 7443, 3996, 6264, 4176}, 50, 6174] (* Paolo Xausa, Jan 24 2026 *)

Prog

(PARI) a(n)=if(n>5, 6174, [8127, 7443, 3996, 6264, 4176][n]) \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Cf. A099009, A151947, A151949, A151951, A151955, A151956, A151967. A151968.

Sequence in context: A209845 A025288 A025306 * A229381 A147633 A237145

Adjacent sequences: A151943 A151944 A151945 * A151947 A151948 A151949

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Aug 18 2009

Status

approved