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 A359357 #26 Feb 07 2023 12:43:07
%S A359357 1,2,2,3,3,3,3,4,5,6,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,9,10,10,10,
%T A359357 11,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,14,14,14,
%U A359357 14,14,14,14,14,15,15,15,15,15,16,17,17,17,17,17,18,18,18,18,18,18,18,19,19,19,19
%N A359357 Number of different ratios between consecutive prime gaps among the first n primes.
%C A359357 What about the asymptotic behavior of a(n), and upper and lower bounds?
%F A359357 a(n) = #{A001223(i+1)/A001223(i)}, i < n-1, where A001223 are prime gaps.
%p A359357 P:= [seq(ithprime(i),i=1..102)]:
%p A359357 G:= P[2..-1]-P[1..-2]:
%p A359357 R:= G[2..-1] /~ G[1..-2]:
%p A359357 seq(nops(convert(R[1..n],set)),n=1..100); # _Robert Israel_, Jan 25 2023
%t A359357 g[m_]:=(Prime[m+2]-Prime[m+1])/(Prime[m+1]-Prime[m]);
%t A359357 Table[Tally[g[Range[j]]]//Length,{j,1,2^7}]
%o A359357 (PARI) f(n) = (prime(n+2)-prime(n+1))/(prime(n+1)-prime(n)); \\ A274263
%o A359357 a(n) = #Set(vector(n, k, f(k))); \\ _Michel Marcus_, Dec 28 2022
%Y A359357 Cf. A001223, A272863, A274225, A274263, A275785.
%K A359357 nonn
%O A359357 3,2
%A A359357 _Andres Cicuttin_, Dec 27 2022