A214559 - OEIS

%I #31 Apr 06 2015 06:58:11

%S 97508421,9753086421,9975084201,975330866421,997530864201,

%T 999750842001,97533308666421,97755108844221,99753308664201,

%U 99975308642001,99997508420001,9753333086666421,9775531088644221,9975333086664201,9977551088442201,9997533086642001,9999753086420001

%N Subsequence of fixed points A099009 of the Kaprekar mapping with numbers of the form 9(x1+1)//8(x2)//7(x3+1)//6(x2)//5(x3+1)//4(x2)//3(x4)//2(x2)//1(x3)//0//9(x2)//8(x3+1)//7(x2)//6(x4)//5(x2)//4(x3+1)//3(x2)//2(x3+1)//1(x2)//0(x1)//1.

%C The sign // denotes concatenation of digits in the definition, and d(x) denotes x repetitions of d, x>=0.

%C Adding digits that share the same "x_i" parameter (where i=1,2,3,4) yields sums divisible by 9 (that is, with the digital root being equal to 9): i=1, 9+0=9; i=2, 8+6+4+2+9+7+5+3+1=45; i=3, 7+5+1+8+4+2=27; i=4, 3+6=9. - _Alexander R. Povolotsky_, Mar 19 2015

%H Syed Iddi Hasan, <a href="/A214559/b214559.txt">Table of n, a(n) for n = 0..9554</a>

%F If d(x) denotes x repetitions of the digit d, then a(n)=9(x1+1)8(x2)7(x3+1)6(x2)5(x3+1)4(x2)3(x4)2(x2)1(x3)09(x2)8(x3+1)7(x2)6(x4)5(x2)4(x3+1)3(x2)2(x3+1)1(x2)0(x1)1, where x1,x2,x3,x4>=0.

%e 9753086421 is a fixed point of the mapping for x1=0, x2=0, x3=0, x4=1.

%Y Cf. A214555, A214556, A214557, A214558.

%K nonn,base

%O 0,1

%A _Syed Iddi Hasan_, Jul 20 2012

%E More terms using b-file by _Michel Marcus_, Mar 27 2015