A102723 Smallest prime a(n) such that a(n)-x and a(n)+x, for x=1 to n, are all composite.

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

Offset

1,1

Comments

a(2n+1)=a(2n). - Robert G. Wilson v, Feb 22 2005

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

David A. Corneth, Table of n, a(n) for n = 1..479 (first 97 terms from Harvey P. Dale)

W. Sierpiński, Remarque sur la répartition des nombres premiers, Colloq. Math., 1 (1948), 193-194.

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

Cf. A007510, A023186.

Sequence in context: A233756 A002582 A368425 * A136146 A289278 A167804

Adjacent sequences: A102720 A102721 A102722 * A102724 A102725 A102726

Keyword

nonn

Author

Ray G. Opao, Feb 06 2005

Extensions

a(12)-a(40) from Robert G. Wilson v, Feb 22 2005

Status

approved