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 A033157 #24 Feb 16 2025 08:32:36 %S A033157 1,4,5,8,10,13,14,17,28,31,32,35,37,40,41,44,82,85,86,89,91,94,95,98, %T A033157 109,112,113,116,118,121,122,125,244,247,248,251,253,256,257,260,271, %U A033157 274,275,278,280,283,284,287,325,328,329,332,334,337,338,341,352,355,356,359,361 %N A033157 Begins with (1, 4); avoids 3-term arithmetic progressions. %C A033157 Also called Stanley Sequence S[1,4]. - _Ralf Stephan_, Jan 31 2014 %D A033157 F. Iacobescu, 'Smarandache Partition Type and Other Sequences.' Bull. Pure Appl. Sci. 16E, 237-240, 1997. %D A033157 H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183. %H A033157 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NonarithmeticProgressionSequence.html">Nonarithmetic Progression Sequence</a> %H A033157 <a href="http://oeis.org/index/No#non_averaging">Index entries related to non-averaging sequences</a> %F A033157 Partial sums of Da(n), where Da(n) is defined in the PARI program. %F A033157 a(n) = A004793(n) + [n is even] + [ceiling(n/2) is even]. Proof by Lawrence Sze. - _Ralf Stephan_, Nov 15 2004 %F A033157 a(n) = A033161(n) - 1 = A185256(n) + 1. - _Ralf Stephan_, Jan 31 2014 %o A033157 (PARI) Da(n)=if(n<1,1,if(n%2==0,3*Da(n/2)+5-13*((n/2)%2)-6*((n/2)%4==2),3)) /* _Ralf Stephan_ */ %Y A033157 Cf. A092482, A004793. Row 2 of array in A093682. %K A033157 nonn,easy %O A033157 1,2 %A A033157 _N. J. A. Sloane_