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 A269132 #28 Sep 08 2022 08:46:15
%S A269132 0,1,4,7,11,16,21,28,35,43,52,61,72,83,95,108,121,136,151,167,184,201,
%T A269132 220,239,259,280,301,324,347,371,396,421,448,475,503,532,561,592,623,
%U A269132 655,688,721,756,791,827,864,901,940,979,1019,1060,1101,1144,1187,1231
%N A269132 a(n) = n + floor(n*(2*n+1)/5).
%C A269132 Differences between the two adjacent prime terms (i.e. between two primes in the blocks of length two) are divisible by 4 (checked up to n=10^8).
%H A269132 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1).
%F A269132 G.f.: (x^6-x^5-x^4-2x^2-x)/((x-1)^3*(x^4+x^3+x^2+x+1)).
%F A269132 a(n) = ceiling(((n*(n+2)+(n+1)*ceiling(n))*(n-1))/ (2*ceiling(n)+ceiling(ceiling(n)+n)+n)+n) for n>0.
%F A269132 a(n) = floor(A139570(n)/5). - _Michel Marcus_, Mar 03 2016
%t A269132 Table[Floor[2 n (n + 3)/5], {n, 0, 1000}]
%t A269132 LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {0, 1, 4, 7, 11, 16, 21}, 100]
%t A269132 CoefficientList[Series[(x^6 - x^5 - x^4 - 2 x^2-x)/((x - 1)^3 (x^4 + x^3 + x^2 + x + 1)), {x, 0, 100}], x]
%o A269132 (PARI) a(n) = 2*n*(n+3)\5; \\ _Michel Marcus_, Mar 03 2016
%o A269132 (Magma) [n + n*(2*n+1) div 5: n in [0..60]]; // _Bruno Berselli_, Mar 03 2016
%Y A269132 Cf. A139570.
%K A269132 nonn,easy
%O A269132 0,3
%A A269132 _Mikk Heidemaa_, Feb 19 2016