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

1, 23, 163, 281, 431, 613, 827, 2003, 2377, 3221, 3691, 6521, 7877, 10151, 10973, 11827, 12713, 17623, 18701, 23333, 24571, 25841, 27143, 28477, 38711, 43577, 45263, 48731, 50513, 65921, 72227, 81083, 85703, 95327, 97813, 102881, 124433

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Alonso del Arte, Ulam spiral (2009). [Note that "East" and "West" in this video match the cover of Scientific American, but "North" and "South" are switched.]

BackIssues.com, Scientific American March 1964 back issue

MathWorld, Prime Spiral

Scientific American, March 1964 cover

Wikipedia, Ulam Spiral

Formula

Positive numbers of the form 4n^2 + 3n + 1 with no more than two divisors.

Mathematica

Select[Table[4 n^2 + 3 n + 1, {n, 0, 199}], Length[Divisors[ # ]] < 3 &]

Crossrefs

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.

Sequence in context: A214895 A042022 A142091 * A155842 A248698 A186260

Adjacent sequences: A168024 A168025 A168026 * A168028 A168029 A168030

Keyword

easy,nonn

Author

Alonso del Arte, Nov 16 2009

Status

approved