cp's OEIS Frontend

A168027 Noncomposite numbers in the southern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.

%I A168027 #18 Feb 16 2025 08:33:11
%S A168027 1,23,163,281,431,613,827,2003,2377,3221,3691,6521,7877,10151,10973,
%T A168027 11827,12713,17623,18701,23333,24571,25841,27143,28477,38711,43577,
%U A168027 45263,48731,50513,65921,72227,81083,85703,95327,97813,102881,124433
%N A168027 Noncomposite numbers in the southern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
%H A168027 G. C. Greubel, <a href="/A168027/b168027.txt">Table of n, a(n) for n = 0..1000</a>
%H A168027 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 A168027 BackIssues.com, <a href="http://backissues.com/issue/Scientific-American-March-1964">Scientific American March 1964 back issue</a>
%H A168027 MathWorld, <a href="https://mathworld.wolfram.com/PrimeSpiral.html">Prime Spiral</a>
%H A168027 Scientific American, <a href="/A168022/a168022.pdf">March 1964 cover</a>
%H A168027 Wikipedia, <a href="https://en.wikipedia.org/wiki/Ulam_spiral#Construction">Ulam Spiral</a>
%F A168027 Positive numbers of the form 4n^2 + 3n + 1 with no more than two divisors.
%t A168027 Select[Table[4 n^2 + 3 n + 1, {n, 0, 199}], Length[Divisors[ # ]] < 3 &]
%Y A168027 Cf. A033951, all numbers of the form 4n^2 + 3n + 1. 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 southwestern ray are in A168026. There are no primes on the southeastern ray, which, being A016754, are the odd squares, and thus none of them are prime.
%K A168027 easy,nonn
%O A168027 0,2
%A A168027 _Alonso del Arte_, Nov 16 2009