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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 (list; graph; refs; listen; history; text; internal format)
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(#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
Sequence in context: A121799 A078034 A181091 * A138770 A006018 A152666
KEYWORD
nonn,more
AUTHOR
Daniel Tisdale, Jun 19 2009
EXTENSIONS
a(15)-a(21) from Michel Marcus, Aug 15 2022
STATUS
approved

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Last modified March 29 06:12 EDT 2024. Contains 371265 sequences. (Running on oeis4.)