A069898 Smallest one of largest prime divisors of all composite numbers between p and next prime.

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

Offset

2,1

Links

Table of n, a(n) for n=2..93.

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.

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}]

Crossrefs

Cf. A020639, A006530, A052180, A052248.

Sequence in context: A103509 A361929 A252941 * A245511 A259940 A228829

Adjacent sequences: A069895 A069896 A069897 * A069899 A069900 A069901

Keyword

nonn

Author

Labos Elemer, Apr 10 2002

Status

approved