%I #7 Aug 15 2022 14:44:18

%S 1,1,2,4,2,12,7,3,3,61,28,15,37,217,206,8,93,460,4,253,738

%N The multiplicity of successive elements of sequence A005250 (increasing prime gaps) as they occur in A161794, the largest prime gap less than (n+1)^2.

%C Sequence A161794 suggests the size of prime gaps grows slower than the size of square intervals, lending credence to Legendre's conjecture.

%e A161794 begins 1, 2, 4, 4, 6, 6, 6, 6, ... that is, 1 one, 1 two, 2 four, 4 six, ... so this sequence begins 1, 1, 2, 4, ...

%o (PARI) f(n) = my(vp = primes(primepi((n+1)^2))); vecmax(vector(#vp-1, k, vp[k+1] - vp[k])); \\ A161794

%o lista(nn) = my(v = vector(nn, k, f(k))); my(list = List(), last = v[1], nb=1); for (n=2, #v, if (v[n] == last, nb++, listput(list, nb); nb = 1; last = v[n];);); Vec(list); \\ _Michel Marcus_, Aug 15 2022

%Y Cf. A005250, A161794.

%K nonn,more

%O 1,3

%A _Daniel Tisdale_, Jun 19 2009

%E a(15)-a(21) from _Michel Marcus_, Aug 15 2022