A214559 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.

97508421, 9753086421, 9975084201, 975330866421, 997530864201, 999750842001, 97533308666421, 97755108844221, 99753308664201, 99975308642001, 99997508420001, 9753333086666421, 9775531088644221, 9975333086664201, 9977551088442201, 9997533086642001, 9999753086420001

Offset: 0

Author

Syed Iddi Hasan, Jul 20 2012

Keywords

• nonn
• base

Comments

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

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

Examples

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

Links

• Syed Iddi Hasan, Table of n, a(n) for n = 0..9554

Crossrefs

Cf. A214555, A214556, A214557, A214558.

Formula

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.

Extensions

More terms using b-file by Michel Marcus, Mar 27 2015