A051650 Lonely numbers: distance to closest prime sets a new record.

0, 23, 53, 120, 211, 1340, 1341, 1342, 1343, 1344, 2179, 3967, 15704, 15705, 16033, 19634, 19635, 24281, 31428, 31429, 31430, 31431, 31432, 31433, 38501, 58831, 155964, 203713, 206699, 370310, 370311, 370312, 370313, 370314, 370315, 370316

Offset

0,2

Links

Charles R Greathouse IV and Giovanni Resta, Table of n, a(n) for n = 0..211 (terms < 10^14, first 156 terms from Charles R Greathouse IV)

Example

23 is 4 units away from the closest prime (not including itself), so 23 is in the sequence.

Mathematica

d[0] = 2; d[k_] := Min[k - NextPrime[k, -1], NextPrime[k] - k]; a[0] = 0; a[n_] := a[n] = (k = a[n-1] + 1; record = d[a[n-1]]; While[d[k] <= record, k++]; k); Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jan 16 2012 *)
dcp[n_]:=Min[n-NextPrime[n, -1], NextPrime[n]-n]; DeleteDuplicates[Table[{n, dcp[n]}, {n, 0, 375000}], GreaterEqual[#1[[2]], #2[[2]]]&][[;; , 1]] (* Harvey P. Dale, Feb 23 2023 *)

Prog

(PARI) print1(0); w=2; p=2; q=3; forprime(r=5, 1e9, if(p+w+w<q, for(t=p+w+1, (q+p)\2, print1(", "t)); w=(q-p)\2); t=min(q-p, r-q); if(t>w, w=t; print1(", "q)); p=q; q=r) \\ Charles R Greathouse IV, Jan 16 2012

Crossrefs

Related sequences: A023186-A023188, A046929-A046931, A051650, A051652, A051697-A051702, A051728-A051730.

Distances are in A051730.

Sequence in context: A132235 A277993 A339188 * A049438 A078854 A078959

Adjacent sequences: A051647 A051648 A051649 * A051651 A051652 A051653

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Dec 23 1999 and from Jud McCranie, Jun 16 2000

Status

approved