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

0,2

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 + 1 with no more than two divisors.

Mathematica

Select[Table[4 n^2 + 1, {n, 0, 99}], Length[Divisors[ # ]] < 3 &]

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.

Sequence in context: A145012 A360204 A147204 * A121326 A347300 A212876

Adjacent sequences: A168021 A168022 A168023 * A168025 A168026 A168027

Keyword

easy,nonn

Author

Alonso del Arte, Nov 16 2009

Status

approved