|
|
A023188
|
|
Lonely (or isolated) primes: least prime of distance n from nearest prime (n = 1 or even).
|
|
18
|
|
|
2, 5, 23, 53, 409, 293, 211, 1847, 3137, 2179, 3967, 23719, 16033, 40387, 44417, 24281, 158699, 220973, 172933, 321509, 38501, 58831, 203713, 268343, 206699, 829399, 824339, 413353, 2280767, 2305549, 3253631, 1272749, 2401807, 2844833, 3021241
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
a(1)=least prime of distance 1 from nearest prime.
if n>1 a(n)=least prime of distance 2n-2 from nearest prime.
|
|
LINKS
|
Abhimanyu Kumar and Anuraag Saxena, Insulated primes, arXiv:2011.14210 [math.NT], 2020. Mentions this sequence.
|
|
MATHEMATICA
|
NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; a = Table[0, {35}]; p = 2; q = 3; k = 1; Do[r = NextPrim[q]; m = Min[r - q, q - p]/2; If[m < 35 && a[[m]] == 0, a[[m]] = q]; p = q; q = r, {n, 1, 235000}]
Join[{2}, Transpose[Flatten[Table[Select[Partition[Prime[ Range[ 1000000]], 3, 1], Min[ Differences[#]] == 2n&, 1], {n, 40}], 1]][[2]]](* Harvey P. Dale, Nov 17 2013 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|