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A051650
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Lonely numbers: distance to closest prime sets a new record.
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18
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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
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OFFSET
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0,2
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LINKS
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EXAMPLE
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23 is 4 units away from the closest prime (not including itself), so 23 is in the sequence.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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