

A161795


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.


0



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

1,3


COMMENTS

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


LINKS



EXAMPLE

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, ...


PROG

(PARI) f(n) = my(vp = primes(primepi((n+1)^2))); vecmax(vector(#vp1, k, vp[k+1]  vp[k])); \\ A161794
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


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



