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A096025 Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 6 and (n+7) mod 9 <> 1.

%I A096025 #13 Sep 08 2022 08:45:14
%S A096025 843,1683,3363,4203,5883,6723,8403,9243,10923,11763,13443,14283,15963,
%T A096025 16803,18483,19323,21003,21843,23523,24363,26043,26883,28563,29403,
%U A096025 31083,31923,33603,34443,36123,36963,38643,39483,41163,42003,43683
%N A096025 Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 6 and (n+7) mod 9 <> 1.
%C A096025 Numbers n such that n mod 840 = 3 and n mod 2520 <> 3.
%H A096025 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A096025 a(n) = -3*(209+70*(-1)^n-420*n). a(n) = a(n-1)+a(n-2)-a(n-3). G.f.: 3*x*(279*x^2+280*x+281) / ((x-1)^2*(x+1)). - _Colin Barker_, Apr 11 2013
%e A096025 843 mod 2 = 844 mod 3 = 845 mod 4 = 846 mod 5 = 847 mod 6 = 848 mod 7 = 849 mod 8 = 1 and 850 mod 9 = 4, hence 843 is in the sequence.
%t A096025 LinearRecurrence[{1,1,-1},{843,1683,3363},40] (* _Harvey P. Dale_, Nov 22 2015 *)
%o A096025 (PARI) {k=7;m=44000;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 A096025 (Magma) [n: n in [1..44000] | forall{j: j in [0..6] | IsOne((n+j) mod (2+j)) and (n+7) mod 9 ne 1}]; // _Bruno Berselli_, Apr 11 2013
%Y A096025 Cf. A007310, A017629, A096022, A096023, A096024, A096026, A096027.
%K A096025 nonn,easy
%O A096025 1,1
%A A096025 _Klaus Brockhaus_, Jun 15 2004