Prime Spirals
I knew I had to make Ulam spirals when I saw Numberphile’s video about them. I wrote Python code to generate these where colors alternate with each concentric square. I made a GitHub repository for the code. A visit to a page of Matthew Conroy gave me the notion to map sequences other than primes too. Factorials, the Fibonacci sequence, and Mersenne primes make for sparse Ulam spirals, but I like them for that fact that they show which sequences are spread far out. For each sequence, there are four images for the numbers 1–10,201, 1–160,801, 1–361,201, and 1–1,002,001.
I made a few I found at the OEIS browse page when I watched for sequences that would fit this type, which, as it turned out, Ulam spirals transmuted from sequences to QR codes.😛
- A030513 Numbers with 4 divisors.
- A037003 Positions of the digit 4 in the decimal expansion of 𝜋.
- A050704 Composite numbers k with the property that k minus the sum of the prime factors of k is prime.
Image Gallery
Click or tap a thumbnail for the full resolution.
prime 10,201
prime 160,801
prime 361,201
prime 1,002,001
square 10,201
square 160,801
square 361,201
square 1,002,001
triangular 10,201
triangular 160,801
triangular 361,201
triangular 1,002,001
pentagonal 10,201
pentagonal 160,801
pentagonal 361,201
pentagonal 1,002,001
hexagonal 10,201
hexagonal 160,801
hexagonal 361,201
hexagonal 1,002,001
heptagonal 10,201
heptagonal 160,801
heptagonal 361,201
heptagonal 1,002,001
octogonal 10,201
octogonal 160,801
octogonal 361,201
octogonal 1,002,001
nonagonal 10,201
nonagonal 160,801
nonagonal 361,201
nonagonal 1,002,001
decagonal 10,201
decagonal 160,801
decagonal 361,201
decagonal 1,002,001
hendecagonal 10,201
hendecagonal 160,801
hendecagonal 361,201
hendecagonal 1,002,001
dodecagonal 10,201
dodecagonal 160,801
dodecagonal 361,201
dodecagonal 1,002,001
factorial 10,201
factorial 160,801
factorial 361,201
factorial 1,002,001
Fibonacci sequence 10,201
Fibonacci sequence 160,801
Fibonacci sequence 361,201
Fibonacci sequence 1,002,001
Mersenne prime 10,201
Mersenne prime 160,801
Mersenne prime 361,201
Mersenne prime 1,002,001
A030513 numbers with 4 divisors 10,201
A030513 numbers with 4 divisors 160,801
A030513 numbers with 4 divisors 361,201
A030513 numbers with 4 divisors 1,002,001
A037003 positions of the digit 4 in the decimal expansion of 𝜋 10,201
A037003 positions of the digit 4 in the decimal expansion of 𝜋 160,801
A037003 positions of the digit 4 in the decimal expansion of 𝜋 361,201
A037003 positions of the digit 4 in the decimal expansion of 𝜋 1,002,001
A050704 composite numbers k with the property that k minus the sum of the prime factors of k is prime 10,201
A050704 composite numbers k with the property that k minus the sum of the prime factors of k is prime 160,801
A050704 composite numbers k with the property that k minus the sum of the prime factors of k is prime 361,201
A050704 composite numbers k with the property that k minus the sum of the prime factors of k is prime 1,002,001