A161795 - OEIS

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.

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

Table of n, a(n) for n=1..21.

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(#vp-1, 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

Cf. A005250, A161794.

Sequence in context: A121799 A078034 A181091 * A138770 A006018 A152666

Adjacent sequences: A161792 A161793 A161794 * A161796 A161797 A161798

KEYWORD

nonn,more

AUTHOR

Daniel Tisdale, Jun 19 2009

EXTENSIONS

a(15)-a(21) from Michel Marcus, Aug 15 2022

STATUS

approved