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User:Matej Veselovac

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The OEIS has a lot of cool sequences. Here are some examples I dabbled with:

■ Some sequences which hide Sierpińsk-ish fractals:

  • A327853 (Sierpiński's triangle × triangular numbers)
  • A327889 (Pascal's triangle ° digit transformation)

■ Noteworthy rare primes (conjectured to be infinite):

  • A000000 (Wall-Sun-Sun primes - none are known)

■ Consecutive palindromes problem:

  • A279092 (k>=2, the double palindromes)
  • A279093 (k>=3, the triple palindromes)
  • A323742 (k=3, the existence problem)
  • A333512 (k=3, but no other palindromic bases)
  • A327810 (irregular consecutive palindromes)

■ Number formation with basic operations (+,-,*,/) problem:

  • A142153 (use integers at most once)
  • A309885 (use integers exactly once)
  • A309886 (use powers of two exactly once)

■ Memorable "Jumping" sequences:

■ Counting on Circles:

  • A250001 (arrangements in affine plane)
  • A067310 (chords with k simple intersections)
  • A331702 (intersections on polygons)

■ Counting with Dominoes:

  • A004003 (count domino tilings of 2n X 2n square)
  • A333837 (count ways to collapse a triangular formation)

■ Sums of (unordered) factorizations:

  • A337037 (numbers with all unique sums)
  • A337080 (numbers with some duplicate sums)
  • A337081 (primitive complement of such numbers)

■ Puzzle-related sequences: