This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380139 #16 Jan 26 2025 09:08:38 %S A380139 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, %T A380139 30,28,26,34,32,36,6,2,4,12,10,8,18,14,16,20,22,24,30,28,26,36,32,34, %U A380139 40,38,42,52,44,50,46,54,58,48,56,60,62,64,72 %N 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. %C A380139 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, ... . %H A380139 Hugo Pfoertner, <a href="/A380139/b380139.txt">Table of n, a(n) for n = 1..583</a> %e A380139 The triangle begins, with corresponding counts in [...]: %e A380139 [2, 1, 1] %e A380139 2, 1, 4, %e A380139 [7, 7, 6, 1] %e A380139 4, 6, 2, 8, %e A380139 [37, 32, 27, 16, 14, 8, 7, 1, 1] %e A380139 6, 4, 2, 10, 8, 12, 14, 18, 20 %e A380139 [255, 170, 162, 103, 98, 86, 47, 39, 33, 16, 15, 14, 11, 5, 3, 3, 1, 1] %e A380139 6, 2, 4, 10, 12, 8, 14, 18, 16, 22, 24, 20, 30, 28, 26, 34, 32, 36, %e A380139 [1641, 1018, 1013, 860, 797, 672, 474, 430, 306, 223, 207, 191, 135, 93, 85, ...] %e A380139 6, 2, 4, 12, 10, 8, 18, 14, 16, 20, 22, 24, 30, 28, 26, ... %e A380139 [11609, 7040, 6945, 6928, 6163, 4796, 4395, 3749, 2542, 2476, 2164, 1949, ...] %e A380139 6, 12, 2, 4, 10, 8, 18, 14, 16, 24, 20, 22, ... %e A380139 6, 12, 2, 4, 10, 18, 8, 14, 24, 16, 30, 20, 22, 28, 26, 36, 42, 34, ... %e A380139 6, 12, 4, 2, 10, 18, 8, 14, 24, 30, 16, 20, 22, 28, 26, 36, 42, 34, ... %e A380139 6, 12, 10, 4, 2, 18, 8, 14, 24, 30, 16, 20, 22, 28, 36, 26, 42, 34, ... %e A380139 6, 12, 18, 10, 2, 4, 8, 24, 30, 14, 20, 16, 22, 36, 28, 26, 42, 34, ... %Y A380139 Cf. A001223, A028334, A038460, A354604. %Y A380139 Cf. A005597, A173557, A305444 for the asymptotic behavior of gap sizes. %K A380139 nonn,tabf %O A380139 1,1 %A A380139 _Hugo Pfoertner_ based on an idea by _Richard Stephen Donovan_, Jan 23 2025