|
|
A102723
|
|
Smallest prime a(n) such that a(n)-x and a(n)+x, for x=1 to n, are all composite.
|
|
4
|
|
|
5, 23, 23, 53, 53, 211, 211, 211, 211, 211, 211, 1847, 1847, 2179, 2179, 2179, 2179, 3967, 3967, 16033, 16033, 16033, 16033, 24281, 24281, 24281, 24281, 24281, 24281, 38501, 38501, 38501, 38501, 38501, 38501, 38501, 38501, 38501, 38501, 58831
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Using Dirichlet's theorem, Sierpiński (1948) proved that a(n) exists for all n > 0. He noted that a(n) is a non-twin prime (A007510), except for a(1) = 5. - Jonathan Sondow, Oct 27 2017
|
|
LINKS
|
|
|
MATHEMATICA
|
f[n_] := Block[{k = 1}, While[ Union[ PrimeQ /@ Sort[ Flatten[ Table[{Prime[k] - i, Prime[k] + i}, {i, n}]]]] != {False}, k++ ]; Prime[k]]; Table[ f[n], {n, 40}] (* Robert G. Wilson v, Feb 22 2005 *)
cmpgap[n_]:=Module[{p=Prime[n]}, Min[p-NextPrime[p, -1], NextPrime[p]-p]]; Module[{nn=10000, prs}, prs=Table[{Prime[n], cmpgap[n]}, {n, nn}]; Table[ SelectFirst[ prs, #[[2]]>=k&], {k, 2, 50}]][[All, 1]] (* Harvey P. Dale, Oct 15 2021 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|