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

Offset: 1

Author

Daniel Tisdale, Jun 19 2009

Keywords

• nonn
• more

Comments

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

Examples

			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, ...
		

Crossrefs

Cf. A005250, A161794.

Programs

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

Extensions

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