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A069898
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Smallest one of largest prime divisors of all composite numbers between p and next prime.
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1
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2, 3, 2, 3, 2, 3, 5, 3, 5, 2, 5, 7, 5, 3, 3, 5, 2, 7, 3, 5, 3, 7, 3, 5, 17, 7, 3, 7, 5, 2, 5, 23, 3, 5, 11, 3, 11, 7, 7, 5, 7, 3, 7, 11, 5, 3, 5, 19, 11, 13, 5, 3, 2, 13, 11, 5, 11, 7, 47, 3, 5, 11, 13, 7, 3, 7, 7, 29, 7, 17, 5, 23, 5, 19, 3, 7, 5, 5, 13, 7, 13, 3, 23, 7, 7, 5, 17, 11, 29, 13, 3, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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EXAMPLE
| n=128:p(128)=719,p(129)=727,d=8; composites between 2 primes:{720,721,722,723,724,725,726}; factor-sets:(2,3,5),(7,103),(2,19),(3,241),(2,3,181),(5,29),(2,3,11) least factors:{2,7,2,3,2,5,2}; Min&Max = {2,7}; largest factors:{5,103,241,181,29,11}; Min&Max = {5,241}; max-of-least=A052180(128)=7, max-of-largest=A052248(128)=241, a(128)=min-of-largest=A069898(128)=5.
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MATHEMATICA
| ffi[x_] := Flatten[FactorInteger[x]]; lf[x_] := Length[FactorInteger[x]]; ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}]; ep[x_] := Table[Part[ffi[x], 2*w], {w, 1, lf[x]}]; mif[x_] := Min[ba[x]]; maf[x_] := Max[ba[x]]; Table[Min[Table[maf[w], {w, Prime[n]+1, Prime[n+1]-1}]], {n, 1, 128}]
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CROSSREFS
| Cf. A020639, A006530, A052180, A052248.
Sequence in context: A114108 A073820 A103509 * A007978 A096737 A165005
Adjacent sequences: A069895 A069896 A069897 * A069899 A069900 A069901
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Apr 10 2002
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