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

Author

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

Keywords

• nonn

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. One 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 A051699.)

Crossrefs

Cf. A051728, A051699.

Programs

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);

Formula

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