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 A002960 M1346 #67 May 03 2024 10:32:02
%S A002960 2,5,8,12,17,22,28,34,41,48,56,65,74,84,94,105,116,128,140,153,166,
%T A002960 180,194,209,224,240,257,274,292,310,329,348,368,388,409,430,452,474,
%U A002960 497,520,544,568,593,618,644,670,697,724,752,780,809,838,868,898,929,960,992,1025,1058,1092,1126,1161,1196
%N A002960 The square sieve.
%C A002960 See example for the construction used.
%C A002960 Conjecture: The first differences are given by A274089 (omitting the first two terms 1 and 2). - _Alisa Ediger_, Jun 04 2016
%D A002960 David L. Silverman, Problem #116, The Square Sieve, J. Rec. Math., 4 (1971), 288-289.
%D A002960 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002960 Sean A. Irvine, <a href="/A002960/b002960.txt">Table of n, a(n) for n = 1..1000</a>
%H A002960 <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%F A002960 Conjecture: a(n) = a(n-1) + 1 + floor(sqrt(a(n-1) + 1 + floor(sqrt(a(n-1))))); a(1) = 2. - _Gionata Neri_, Jun 22 2015
%F A002960 Conjecture: a(n) = 2^(x-1)*(2^(x-1)+y-1) + floor((y+1)^2/4), where y = n+1+x-2^x and x = floor(log_2(n+1+floor(log_2(n)))). - _Gionata Neri_, Jul 05 2015
%e A002960 Start with
%e A002960 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,...
%e A002960 Remove all square-th terms, 1,4,9,16,... to get
%e A002960 2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,...
%e A002960 Return 2 as the first term in the sequence and remove it to get
%e A002960 3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,...
%e A002960 Remove the 1st,4th,9th,16th,... terms to get
%e A002960 5,6,8,10,11,12,14,15,17,18,19,20,22,23,...
%e A002960 Return 5 as the next term in the sequence and remove it to get
%e A002960 6,8,10,11,12,14,15,17,18,19,20,22,23,...
%e A002960 Remove the 1st,4th,9th,16th,... terms to get
%e A002960 8,10,12,14,15,17,19,20,22,23,...
%e A002960 Return 8 as the next term in the sequence and remove it to get
%e A002960 10,12,14,15,17,19,20,22,23,...
%e A002960 Remove the 1st,4th,9th,16th,... terms to get
%e A002960 12,14,15,19,20,22,23,...
%e A002960 etc. - _Sean A. Irvine_, Dec 10 2014
%p A002960 sieve:= L -> subsop(seq(i^2=NULL, i=1..floor(sqrt(nops(L)))),L):
%p A002960 A:= [$1..10^5]:
%p A002960 for n from 1 do
%p A002960 A:= sieve(A);
%p A002960 if nops(A) = 0 then break fi;
%p A002960 R[n]:= A[1];
%p A002960 A:= subsop(1=NULL,A);
%p A002960 od:
%p A002960 seq(R[i],i=1..n-1); # _Robert Israel_, Dec 11 2014
%t A002960 First /@ NestWhileList[Function[w, {First@ #, Rest@ #} &@ Delete[Last@ w, #] &@ Map[{#} &, Reverse@ Range[Floor@ Sqrt@ Length[Last@ w]]^2]], {0, Range@ 1200}, Length@ Last@ # > 1 &] (* _Michael De Vlieger_, Jun 05 2016 *)
%Y A002960 Cf A274089.
%K A002960 nonn
%O A002960 1,1
%A A002960 _N. J. A. Sloane_