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

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Examples

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

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)

Crossrefs

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

Distances are in A051730.

Programs

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 *)

PARI

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

Extensions

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