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 A266297 #35 Jul 30 2024 06:20:29
%S A266297 0,1,4,9,10,11,14,19,20,21,24,29,30,31,34,39,40,41,44,49,50,51,54,59,
%T A266297 60,61,64,69,70,71,74,79,80,81,84,89,90,91,94,99,100,101,104,109,110,
%U A266297 111,114,119,120,121,124,129,130,131,134,139,140,141,144,149
%N A266297 Numbers whose last digit is a square.
%C A266297 Numbers ending in 0, 1, 4 and 9.
%C A266297 Union of A008592, A017281, A017317 and A017377. - Hurt
%C A266297 None of these numbers are prime in Z[phi] (where phi = 1/2 + sqrt(5)/2 is the golden ratio), since the numbers in this sequence that are prime in Z can be expressed in the form (a - b sqrt(5))(a + b sqrt(5)). - _Alonso del Arte_, Dec 30 2015
%C A266297 Union of A197652 and A016897. - _Wesley Ivan Hurt_, Dec 31 2015
%C A266297 Union of A146763 and A090771. - _Wesley Ivan Hurt_, Jan 01 2016
%H A266297 G. C. Greubel, <a href="/A266297/b266297.txt">Table of n, a(n) for n = 1..5000</a>
%H A266297 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A266297 G.f.: x^2*(1 + 3*x + 5*x^2 + x^3)/((x - 1)^2*(1 + x + x^2 + x^3)).
%F A266297 a(n) = a(n - 1) + (n - 4) - a(n - 5) for n > 5.
%F A266297 a(n) = (10n - 11 + (-1)^n + (4 + 2(-1)^n) * (-1)^((2n - 1 + (-1)^n)/4))/4.
%F A266297 a(n+1) - a(n) = A091084(n+1) for n>0.
%F A266297 Sum_{n>=2} (-1)^n/a(n) = (14*sqrt(5)*arccoth(sqrt(5)) - 2*Pi*sqrt(1-2/sqrt(5)) + 16*log(2) + 5*log(5))/40. - _Amiram Eldar_, Jul 30 2024
%p A266297 A266297:=n->(10*n-11+(-1)^n+(4+2*(-1)^n)*(-1)^((2*n-1+(-1)^n)/4))/4: seq(A266297(n), n=1..100);
%t A266297 Table[(10 n - 11 + (-1)^n + (4 + 2 (-1)^n)*(-1)^((2 n - 1 + (-1)^n)/4))/4, {n, 50}] (* _G. C. Greubel_, Dec 27 2015 *)
%t A266297 LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 4, 9, 10}, 60] (* _Vincenzo Librandi_, Dec 27 2015 *)
%t A266297 CoefficientList[Series[x*(1 + 3*x + 5*x^2 + x^3)/((x - 1)^2*(1 + x + x^2 + x^3)), {x, 0, 100}], x] (* _Wesley Ivan Hurt_, Dec 30 2015 *)
%t A266297 Flatten[Table[10n + {0, 1, 4, 9}, {n, 0, 19}]] (* _Alonso del Arte_, Dec 30 2015 *)
%t A266297 Select[Range[0,150],MemberQ[{0,1,4,9},Mod[#,10]]&] (* _Harvey P. Dale_, Jul 30 2019 *)
%o A266297 (Magma) [(10*n-11+(-1)^n+(4+2*(-1)^n)*(-1)^((2*n-1+(-1)^n) div 4))/4: n in [1..60]]; // _Vincenzo Librandi_, Dec 27 2015
%o A266297 (PARI) is(n) = issquare(n%10); \\ _Altug Alkan_, Dec 29 2015
%Y A266297 Cf. A008592, A016897, A017281, A017317, A017377, A090771, A091084, A141158, A146763, A197652.
%K A266297 nonn,easy,base
%O A266297 1,3
%A A266297 _Wesley Ivan Hurt_, Dec 26 2015