This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A096022 #22 Sep 08 2022 08:45:14
%S A096022 15,27,39,51,75,87,99,111,135,147,159,171,195,207,219,231,255,267,279,
%T A096022 291,315,327,339,351,375,387,399,411,435,447,459,471,495,507,519,531,
%U A096022 555,567,579,591,615,627,639,651,675,687,699,711,735,747,759,771,795
%N A096022 Numbers that are congruent to {15, 27, 39, 51} mod 60.
%C A096022 Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 2 and (n+3) mod 5 <> 1.
%C A096022 This is one of a family of sequences which are defined (or could be defined) according to the same scheme: Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to k-1 and (n+k) mod (2+k) <> 1. We have A007310 for k = 1, A017629 for k = 2, this one (A096022) for k = 3, A096023 for k = 5, A096024 for k = 6, A096025 for k = 7, A096026 for k = 9, A096027 for k = 11. Remarkably these sequences are empty for k = 4, 8, 10, ... (i.e., if k+1 is a term of A080765).
%C A096022 Numbers n such that n mod 12 = 3 and n mod 60 <> 3.
%C A096022 Subsequence of A017557: 12n+3.
%H A096022 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A096022 G.f.: 3*x*(5+4*x+4*x^2+4*x^3+3*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Oct 08 2011
%F A096022 From _Wesley Ivan Hurt_, Jun 04 2016: (Start)
%F A096022 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A096022 a(n) = 3*(10*n-3-i^(2*n)-(1-i)*i^(-n)-(1+i)*i^n)/2 where i=sqrt(-1). (End)
%F A096022 E.g.f.: 3*(3 + sin(x) - cos(x) + (5*x - 1)*sinh(x) - (2 - 5*x)*cosh(x)). - _Ilya Gutkovskiy_, Jun 05 2016
%e A096022 51 mod 2 = 52 mod 3 = 53 mod 4 = 1 and 54 mod 5 = 4, hence 51 is in the sequence; 3 mod 2 = 4 mod 3 = 5 mod 4 = 6 mod 5 = 1, hence 3 is not in the sequence.
%p A096022 A096022:=n->3*(10*n-3-I^(2*n)-(1-I)*I^(-n)-(1+I)*I^n)/2: seq(A096022(n), n=1..80); # _Wesley Ivan Hurt_, Jun 04 2016
%t A096022 Table[3*(10n-3-I^(2n)-(1-I)*I^(-n)-(1+I)*I^n)/2, {n, 80}] (* _Wesley Ivan Hurt_, Jun 04 2016 *)
%o A096022 (PARI) {k=3;m=800;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 A096022 (Magma) [ n : n in [1..1500] | n mod 60 in [15, 27, 39, 51] ] // _Vincenzo Librandi_, Mar 24 2011
%Y A096022 Cf. A007310, A017557, A017629, A080765, A096023, A096024, A096025, A096026, A096027.
%K A096022 nonn,easy
%O A096022 1,1
%A A096022 _Klaus Brockhaus_, Jun 15 2004
%E A096022 New definition from _Ralf Stephan_, Dec 01 2004