A214555 Subsequence of fixed points A099009 of the Kaprekar mapping with numbers of the form 5(n)//4//9(n+1)//4(n)//5.

495, 549945, 554999445, 555499994445, 555549999944445, 555554999999444445, 555555499999994444445, 555555549999999944444445, 555555554999999999444444445, 555555555499999999994444444445, 555555555549999999999944444444445

Offset

0,1

Comments

The symbols // denote concatenation of digits in the definition, and d(n) denotes n repetitions of d, n >= 0.

Conjecture: satisfies a linear recurrence having signature (1111, -112110, 1111000, -1000000). - Harvey P. Dale, Nov 23 2022

Links

Syed Iddi Hasan, Table of n, a(n) for n = 0..165

Formula

If d(n) denotes n repetitions of the digit d, then a(n) = 5(n)49(n+1)4(n)5, where n >= 0.

Example

549945 is a fixed point of the mapping for n=1.

Mathematica

Table[FromDigits[Join[PadRight[{}, n, 5], {4}, PadRight[{}, n+1, 9], PadRight[{}, n, 4], {5}]], {n, 0, 15}] (* Harvey P. Dale, Nov 23 2022 *)

Crossrefs

Cf. A214556-A214559.

Sequence in context: A104478 A133352 A140913 * A333756 A179170 A345351

Adjacent sequences: A214552 A214553 A214554 * A214556 A214557 A214558

Keyword

nonn,base

Author

Syed Iddi Hasan, Jul 20 2012

Status

approved