A096024 - OEIS

%I #11 Sep 08 2022 08:45:14

%S 423,1263,2103,2943,3783,4623,5463,6303,7143,7983,8823,9663,10503,

%T 11343,12183,13023,13863,14703,15543,16383,17223,18063,18903,19743,

%U 20583,21423,22263,23103,23943,24783,25623,26463,27303,28143,28983,29823

%N Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 5 and (n+6) mod 8 <> 1.

%C Numbers n such that n mod 840 = 423.

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 2*a(n-1)-a(n-2). G.f.: 3*x*(139*x+141) / (x-1)^2. - _Colin Barker_, Apr 11 2013

%F a(n) = 840*n-417. [_Bruno Berselli_, Apr 11 2013]

%e 423 mod 2 = 424 mod 3 = 425 mod 4 = 426 mod 5 = 427 mod 6 = 428 mod 7 = 1 and 429 mod 8 = 5, hence 423 is in the sequence.

%o (PARI) {k=6;m=30000;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..30000] | forall{j: j in [0..5] | IsOne((n+j) mod (2+j)) and (n+6) mod 8 ne 1}]; // _Bruno Berselli_, Apr 11 2013

%Y Cf. A007310, A017629, A096022, A096023, A096025, A096026, A096027.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Jun 15 2004