A132860 Smallest number at distance 2n from nearest prime (variant 2).

2, 0, 93, 119, 531, 897, 1339, 1341, 1343, 9569, 15703, 15705, 19633, 19635, 31425, 31427, 31429, 31431, 31433, 155959, 155961, 155963, 360697, 360699, 360701, 370311, 370313, 370315, 370317, 1349591, 1357261, 1357263, 1357265, 1357267

Offset

1,1

Comments

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.)

Links

Table of n, a(n) for n=1..34.

Formula

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

Maple

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);

Crossrefs

Cf. A051728, A051699.

Sequence in context: A216678 A136559 A009740 * A156485 A307946 A009270

Adjacent sequences: A132857 A132858 A132859 * A132861 A132862 A132863

Keyword

nonn

Author

R. J. Mathar, Nov 18 2007, Nov 30 2007

Status

approved