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A132860
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Smallest number at distance 2n from nearest prime (variant 2).
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1
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2, 0, 93, 119, 531, 897, 1339, 1341, 1343, 9569, 15703, 15705, 19633, 19635, 31425, 31427, 31429, 31431, 31433, 155959, 155961, 155963, 360697, 360699, 360701, 370311, 370313, 370315, 370317, 1349591, 1357261, 1357263, 1357265, 1357267
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Let f(m) be the distance to the nearest prime as defined in A051699(m). Then a(n) = min { m: f(m)= 2n }. A051728 uses A051700(m) to define the distance.
Note that the requirement f(m)>=2n yields the same sequence as f(m)=2n here. (Reasoning: We are essentially probing for prime gaps of size 4n or larger while increasing m. On cannot get earlier hits by relaxing the requirement from the equal to the larger-or-equal sign, because m triggers as soon as the distance to the start of the gap reaches 2n, with both definitions. This is an inherent consequence of using A051669.)
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FORMULA
| a(n) = min {m : A051699(m) = 2n}.
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MAPLE
| A051699 := proc(m) if isprime(m) then 0 ; elif m <= 2 then op(m+1, [2, 1]) ; else min(nextprime(m)-m, m-prevprime(m)) ; fi ; end: a := proc(n) local m ; for m from 0 do if A051699(m) = 2 * n then RETURN(m) ; fi ; od: end: seq(a(n), n=0..18);
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CROSSREFS
| Cf. A051728, A051699.
Sequence in context: A156490 A136559 A009740 * A156485 A009270 A033838
Adjacent sequences: A132857 A132858 A132859 * A132861 A132862 A132863
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KEYWORD
| nonn
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AUTHOR
| R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 18 2007, Nov 30 2007
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