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 A168026 #41 Feb 16 2025 08:33:11
%S A168026 1,7,43,73,157,211,421,601,1483,2551,2971,3907,4423,6163,6481,8191,
%T A168026 12211,19183,22651,26407,27061,28393,31153,35533,37057,37831,42643,
%U A168026 47743,55933,60763,71023,74257,77563,83233,84391,98911,110557,113233
%N A168026 Noncomposite numbers in the southwestern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
%C A168026 From _Peter Munn_, Mar 17 2018: (Start)
%C A168026 Noncomposites of the form k^2 + k + 1 with k even and nonnegative (and the same values occur with k odd and negative). Equivalently, noncomposites of the form 4k^2 + 2k + 1 with k >= 0, or 4k^2 - 6k + 3 with k > 0.
%C A168026 A073337 lists those of the form k^2 + k + 1 with k odd and positive, and this is equivalently those of the form 4k^2 - 2k + 1 with k > 0.
%C A168026 (End)
%C A168026 Numbers that are the sum of A000217(2*k-3) + A000217(2*k-1) that result in either unity or a prime, for k,n >= 1. For k,n >= 0, a(n+1) = 4*k*2 + 2*k + 1 will give the same results. - _J. M. Bergot_, May 07 2018
%H A168026 G. C. Greubel, <a href="/A168026/b168026.txt">Table of n, a(n) for n = 1..1000</a>
%H A168026 Alonso del Arte, <a href="http://www.youtube.com/watch?v=dx24qqBc-PY">Ulam spiral</a> (2009). [Note that "East" and "West" in this video match the cover of Scientific American, but "North" and "South" are switched.]
%H A168026 BackIssues.com, <a href="http://backissues.com/issue/Scientific-American-March-1964">Scientific American March 1964 back issue</a>
%H A168026 MathWorld, <a href="https://mathworld.wolfram.com/PrimeSpiral.html">Prime Spiral</a>
%H A168026 Scientific American, <a href="/A168022/a168022.pdf">March 1964 cover</a>
%H A168026 Wikipedia, <a href="https://en.wikipedia.org/wiki/Ulam_spiral#Construction">Ulam Spiral</a>
%F A168026 Numbers of the form 4k^2 - 6k + 3 with k > 0 and no more than two divisors. [corrected by _Peter Munn_, Mar 17 2018]
%t A168026 Select[Table[4 n^2 - 6 n + 3, {n, 200}], Length[Divisors[ # ]] < 3 &]
%o A168026 (PARI) lista(nn) = {print1(1, ", "); for(k=1, nn, if(isprime(p=4*k^2-6*k+3), print1(p, ", ")));} \\ _Altug Alkan_, Mar 22 2018
%Y A168026 Cf. A054569, all numbers of the form 4k^2 - 6k + 3 with k > 0. Noncomposites of the eastern ray are in A168022. Primes of the northeastern ray are in A073337. Noncomposites of the northern ray are in A168023. Primes of the northwestern ray are in A121326. Noncomposites of the western ray are in A168025. Noncomposites of the southern ray are in A168027.
%K A168026 easy,nonn
%O A168026 1,2
%A A168026 _Alonso del Arte_, Nov 16 2009