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A280658
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Numbers ending with their digital root in decimal representation.
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2
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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
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OFFSET
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1,3
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COMMENTS
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10% of the nonnegative integers are in the sequence, approximatively.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,-1).
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FORMULA
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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)
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EXAMPLE
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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.
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MAPLE
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0, seq(10*x-19-9*((x-2) mod 9), x=2..100); # Robert Israel, Apr 23 2017
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n)=if(n==1, 0, n--; 90*((n-1)\9)+(n-1)%9+1) \\ David A. Corneth, Apr 21 2017
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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