A168022 Noncomposite numbers in the eastern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.

1, 2, 11, 53, 127, 233, 541, 743, 977, 1871, 3511, 4001, 4523, 5077, 9851, 11503, 12377, 14221, 16193, 19391, 20521, 21683, 22877, 24103, 29327, 30713, 33581, 42953, 55343, 57241, 63127, 67211, 80231, 84827, 91961, 101921, 104491, 123377

Offset: 0

Author

Alonso del Arte, Nov 16 2009

Keywords

• easy
• nonn

Comments

Although 1 was not considered a prime number in Ulam's time, the March 1964 cover of Scientific American shows 1 highlighted in the same way as the primes.

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

Crossrefs

Cf. A054552, all numbers of the form 4n^2 - 3n + 1. Primes of northeastern ray are in A073337. Noncomposites of the northern ray are in A168023. Noncomposites of the northwestern ray are in A168024. Noncomposites of the western ray are in A168025. Noncomposites of the southwestern ray are in A168026. Noncomposites of the southern ray are in A168027.

Programs

Mathematica

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

Formula

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