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 A375852 #25 Mar 30 2025 04:52:11
%S A375852 0,1,3,6,7,9,12,15,18,19,21,24,25,27,30,33,36,37,39,42,43,45,48,51,54,
%T A375852 55,57,60,61,63,66,69,72,73,75,78,79,81,84,87,90,91,93,96,97,99,102,
%U A375852 105,108,109,111,114,115,117,120,123,126,127,129,132,133,135,138,141,144,145,147,150
%N A375852 Numbers congruent to {0, 1, 3, 6, 7, 9, 12, 15} mod 18.
%C A375852 Appears to be the union of A061641 (pure numbers in the Collatz (3x+1) iteration, also called pure hailstone numbers) and A309180 (unsuspected numbers to check in the Collatz conjecture).
%C A375852 The differences are periodic: 1, 2, 3, 1, 2, 3, 3, 3.
%H A375852 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-2,2,-2,2,-1).
%F A375852 From _Stefano Spezia_, Sep 03 2024: (Start)
%F A375852 G.f.: x^2*(1 + x + 2*x^2 - x^3 + 3*x^4 + 3*x^6)/((1 - x)^2*(1 + x^2 + x^4 + x^6)).
%F A375852 E.g.f.: ((9*x - 14)*cosh(x) + sin(x) + 2*sqrt(2)*cosh(x/sqrt(2))*sin(x/sqrt(2)) + (9*x - 14)*sinh(x) + 2*(6 + cos(x) + (sqrt(2)*cos(x/sqrt(2)) + sin(x/sqrt(2)))*sinh(x/sqrt(2))))/4. (End)
%t A375852 Select[Range[0, 200], MemberQ[{0, 1, 3, 6, 7, 9, 12, 15}, Mod[#, 18]] &] (* _Amiram Eldar_, Aug 31 2024 *)
%Y A375852 Cf. A061641, A309180.
%K A375852 nonn,easy
%O A375852 1,3
%A A375852 _Jules Beauchamp_, Aug 31 2024