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URL: https://oeis.org/A051650

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A051650
Lonely numbers: distance to closest prime sets a new record.
18
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
Distances are in A051730.
Sequence in context: A277993 A339188 A385035 * A049438 A078854 A078959
KEYWORD
nonn,nice
EXTENSIONS
More terms from James Sellers, Dec 23 1999 and from Jud McCranie, Jun 16 2000
STATUS
approved