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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 (list; graph; refs; listen; history; text; internal format)
 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+ww, 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,changed AUTHOR N. J. A. Sloane EXTENSIONS More terms from James A. Sellers, Dec 23 1999 and from Jud McCranie, Jun 16 2000 STATUS approved

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Last modified February 24 21:21 EST 2024. Contains 370307 sequences. (Running on oeis4.)