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URL: https://oeis.org/A069898

⇱ A069898 - OEIS

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A069898
Smallest of the largest prime divisors of all the composite numbers between prime(n) and prime(n+1).
1
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
EXAMPLE
n=128: prime(128) = 719, prime(129) = 727, d = 8; composites between the 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 and Max = {2,7}; largest factors:{5,103,241,181,29,11}; Min and Max = {5,241}; max-of-least = A052180(128) = 7, max-of-largest = A052248(128) = 241, a(128) = min-of-largest = a(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}]
PROG
(PARI) lista(plim) = {my(pmin, prev = 3); forprime(p = 5, plim, pmin = p; for(k = prev+1, p-1, pmin = min(pmin, vecmax(factor(k)[, 1]))); print1(pmin, ", "); prev = p); } \\ Amiram Eldar, Oct 24 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 10 2002
STATUS
approved