1,1

Let f(m) be the distance to the nearest prime as defined in A051699(m). Then a(n) = min { m: f(m)= 2n }. A051728 uses A051700(m) to define the distance.

Note that the requirement f(m)>=2n yields the same sequence as f(m)=2n here. (Reasoning: We are essentially probing for prime gaps of size 4n or larger while increasing m. On cannot get earlier hits by relaxing the requirement from the equal to the larger-or-equal sign, because m triggers as soon as the distance to the start of the gap reaches 2n, with both definitions. This is an inherent consequence of using A051669.)

a(n) = min {m : A051699(m) = 2n}.

A051699 := proc(m) if isprime(m) then 0 ; elif m <= 2 then op(m+1, [2, 1]) ; else min(nextprime(m)-m, m-prevprime(m)) ; fi ; end: a := proc(n) local m ; for m from 0 do if A051699(m) = 2 * n then RETURN(m) ; fi ; od: end: seq(a(n), n=0..18);

Cf. A051728, A051699.

Adjacent sequences: A132857 A132858 A132859 this_sequence A132861 A132862 A132863

Sequence in context: A136558 A136559 A009740 this_sequence A009270 A033838 A046065

nonn

R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 18 2007, Nov 30 2007