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%I #23 Apr 18 2024 18:20:03
%S 2523,5043,7563,10083,12603,15123,17643,20163,22683,25203,30243,32763,
%T 35283,37803,40323,42843,45363,47883,50403,52923,57963,60483,63003,
%U 65523,68043,70563,73083,75603,78123,80643,85683,88203,90723,93243
%N Numbers k such that (k+j) mod (2+j) = 1 for j from 0 to 8 and (k+9) mod 11 <> 1.
%C Numbers k such that k mod 2520 = 3 and k mod 27720 <> 3.
%H Harvey P. Dale, <a href="/A096026/b096026.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,1,-1).
%F G.f.: 3*x*(839*x^10 +840*x^9 +840*x^8 +840*x^7 +840*x^6 +840*x^5 +840*x^4 +840*x^3 +840*x^2 +840*x +841) / ((x -1)^2*(x +1)*(x^4 -x^3 +x^2 -x +1)*(x^4 +x^3 +x^2 +x +1)). - _Colin Barker_, Apr 11 2013
%e 2523 mod 2 = 2524 mod 3 = 2525 mod 4 = 2526 mod 5 = 2527 mod 6 = 2528 mod 7 = 2529 mod 8 = 2530 mod 9 = 2531 mod 10 = 1 and 2532 mod 11 = 2, hence 2523 is in the sequence.
%t Select[Range[94000],Union[Mod[#+Range[0,8],Range[2,10]]]=={1}&&Mod[ #+9,11]!=1&] (* or *) LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1},{2523,5043,7563,10083,12603,15123,17643,20163,22683,25203,30243},40](* _Harvey P. Dale_, Sep 25 2019 *)
%o (PARI) {k=9;m=95000;for(n=1,m,j=0;b=1;while(b&&j<k,if((n+j)%(2+j)==1,j++,b=0));if(b&&(n+k)%(2+k)!=1,print1(n,",")))}
%o (Magma) [n: n in [1..100000] | forall{j: j in [0..8] | IsOne((n+j) mod (2+j)) and (n+9) mod 11 ne 1}]; // _Bruno Berselli_, Apr 11 2013
%Y Cf. A007310, A017629, A096022, A096023, A096024, A096025, A096027.
%K nonn,easy
%O 1,1
%A _Klaus Brockhaus_, Jun 15 2004