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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-Fran├žois Alcover, Jan 16 2012 *)

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: A128473 A132235 A277993 * A049438 A171432 A078854

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

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Last modified August 20 13:04 EDT 2017. Contains 290835 sequences.