The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A280658 Numbers ending with their digital root in decimal representation. 2
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 91, 92, 93, 94, 95, 96, 97, 98, 99, 181, 182, 183, 184, 185, 186, 187, 188, 189, 271, 272, 273, 274, 275, 276, 277, 278, 279, 361, 362, 363, 364, 365, 366, 367, 368, 369, 451, 452, 453, 454, 455, 456, 457, 458, 459, 541, 542, 543, 544, 545, 546, 547, 548, 549, 631, 632, 633 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 10% of the nonnegative integers are in the sequence, approximatively. LINKS Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001 Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,-1). FORMULA From Robert Israel, Apr 23 2017: (Start) a(n) = 10*n-19-9*((n-2) mod 9) for n > 1. G.f.: (x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+81*x^11)/(1-x-x^9+x^10). (End) EXAMPLE The digital root of 91 is 1 and "1" is the last digit of "91", so 91 is in the sequence. The digital root of 90 is 9 and "9" is not the last digit of "90", so 90 is not in the sequence. The digital root of 92 is 2 and "2" is the last digit of "92", so 92 is in the sequence. Etc. MAPLE 0, seq(10*x-19-9*((x-2) mod 9), x=2..100); # Robert Israel, Apr 23 2017 MATHEMATICA dr[n_]:=NestWhile[Total[IntegerDigits[#]]&, n, #>9&]; Select[Range[ 0, 700], Mod[ #, 10]==dr[#]&] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 91}, 100] (* Harvey P. Dale, Aug 20 2021 *) PROG (PARI) a(n)=if(n==1, 0, n--; 90*((n-1)\9)+(n-1)%9+1) \\ David A. Corneth, Apr 21 2017 (PARI) nxt(n) = if((n-1)%9+1==9&&n, n+82, n+1) \\ David A. Corneth, Apr 21 2017 CROSSREFS Cf. A010888. Sequence in context: A345406 A198486 A061805 * A061219 A071271 A066492 Adjacent sequences: A280655 A280656 A280657 * A280659 A280660 A280661 KEYWORD nonn,base AUTHOR Eric Angelini and Jean-Marc Falcoz, Apr 12 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 12 19:26 EDT 2024. Contains 375113 sequences. (Running on oeis4.)