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User: Richard Stephen Donovan

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Richard Stephen Donovan has authored 1 sequences.

A380139 Prime gaps between 10^m and 10^(m+1), m>=0, sorted first by falling number of occurrences and then by rising gap size, written as an irregular triangle.

Original entry on oeis.org

2, 1, 4, 4, 6, 2, 8, 6, 4, 2, 10, 8, 12, 14, 18, 20, 6, 2, 4, 10, 12, 8, 14, 18, 16, 22, 24, 20, 30, 28, 26, 34, 32, 36, 6, 2, 4, 12, 10, 8, 18, 14, 16, 20, 22, 24, 30, 28, 26, 36, 32, 34, 40, 38, 42, 52, 44, 50, 46, 54, 58, 48, 56, 60, 62, 64, 72
Offset: 1

Author

Hugo Pfoertner based on an idea by Richard Stephen Donovan, Jan 23 2025

Keywords

Comments

A gap between two primes p1 and p2 is assumed to belong to the range [10^m .. 10^(m+1)[ if 10^m <= (p1+p2)/2 < 10^(m+1). Thus the gap between 7 and 11 is counted in the interval 1 .. 10. Gaps symmetric to 10^k occur for k = 17, 45, ... .

Examples

			The triangle begins, with corresponding counts in [...]:
  [2, 1, 1]
   2, 1, 4,
  [7, 7, 6, 1]
   4, 6, 2, 8,
  [37, 32, 27, 16, 14,  8,  7,  1,  1]
    6,  4,  2, 10,  8, 12, 14, 18, 20
  [255, 170, 162, 103, 98, 86, 47, 39, 33, 16, 15, 14, 11,  5,  3,  3,  1,  1]
    6,   2,   4,   10, 12,  8, 14, 18, 16, 22, 24, 20, 30, 28, 26, 34, 32, 36,
  [1641, 1018, 1013, 860, 797, 672, 474, 430, 306, 223, 207, 191, 135, 93, 85, ...]
     6,    2,    4,   12,  10,  8,   18,  14,  16,  20,  22,  24,  30, 28, 26, ...
  [11609, 7040, 6945, 6928, 6163, 4796, 4395, 3749, 2542, 2476, 2164, 1949, ...]
     6,    12,    2,    4,   10,    8,   18,   14,   16,   24,   20,   22,  ...
  6, 12, 2, 4, 10, 18, 8, 14, 24, 16, 30, 20, 22, 28, 26, 36, 42, 34, ...
  6, 12, 4, 2, 10, 18, 8, 14, 24, 30, 16, 20, 22, 28, 26, 36, 42, 34, ...
  6, 12, 10, 4, 2, 18, 8, 14, 24, 30, 16, 20, 22, 28, 36, 26, 42, 34, ...
  6, 12, 18, 10, 2, 4, 8, 24, 30, 14, 20, 16, 22, 36, 28, 26, 42, 34, ...
		

Crossrefs

Cf. A005597, A173557, A305444 for the asymptotic behavior of gap sizes.