A228157 Numbers k which are anagrams of k+9.

12, 23, 34, 45, 56, 67, 78, 89, 101, 112, 123, 134, 145, 156, 167, 178, 189, 201, 212, 223, 234, 245, 256, 267, 278, 289, 301, 312, 323, 334, 345, 356, 367, 378, 389, 401, 412, 423, 434, 445, 456, 467, 478, 489, 501, 512, 523, 534, 545, 556, 567, 578, 589

Offset: 1

Author

Alan Bryant, Aug 16 2013

Keywords

• base
• easy
• nonn

Comments

Numbers with at least 2 digits, ending in digits d and d+1 (and d<=8). - Joerg Arndt, Aug 28 2013

First differences are 9-periodic: 11,11,11,11,11,11,11,11,12. - Ralf Stephan, Aug 28 2013

Links

• JungHwan Min, Table of n, a(n) for n = 1..1000

Programs

Magma

[n: n in [0..600] | Sort(Intseq(n)) eq Sort(Intseq(n+9))]; // Bruno Berselli, Jan 08 2016

Mathematica

Reap[Do[If[Sort@IntegerDigits[n] == Sort@IntegerDigits[n + 9], Sow[n]], {n, 500}]][[-1, 1]] (* JungHwan Min, Jan 05 2016 *)
Select[Range[0, 1000], Sort[IntegerDigits[#]] == Sort[IntegerDigits[# + 9]] &] (* Vincenzo Librandi, Jan 06 2016 *)

Formula

From Chai Wah Wu, Dec 23 2016: (Start)

a(n) = a(n-1) + a(n-9) - a(n-10) for n > 10.

G.f.: x*(-x^9 + 12*x^8 + 11*x^7 + 11*x^6 + 11*x^5 + 11*x^4 + 11*x^3 + 11*x^2 + 11*x + 12)/(x^10 - x^9 - x + 1). (End)