A168024 Noncomposite numbers in the northwestern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.

1, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601, 2917, 3137, 4357, 5477, 7057, 8101, 8837, 12101, 13457, 14401, 15377, 15877, 16901, 17957, 21317, 22501, 24337, 25601, 28901, 30977, 32401, 33857

Offset: 0

Author

Alonso del Arte, Nov 16 2009

Keywords

• easy
• nonn

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

Essentially the same sequence as A002496, A121326, A163588.

Cf. A053755, all numbers of the form 4n^2 + 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 (the same as this sequence but without the initial 1). 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 + 1, {n, 0, 99}], Length[Divisors[ # ]] < 3 &]

Formula

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