A082881 Least value of A075860(j) when j runs through composite numbers between n-th and (n+1)-th primes. That is, the smallest fixed-point[=prime] reached by iteration of function A008472(=sum of prime factors) initiated with composite values between two consecutive primes.
0, 2, 5, 2, 5, 2, 5, 7, 2, 7, 2, 2, 5, 2, 2, 2, 7, 2, 2, 5, 2, 3, 2, 5, 3, 13, 2, 5, 3, 2, 2, 2, 3, 2, 7, 5, 3, 13, 2, 3, 7, 2, 5, 3, 2, 2, 2, 2, 5, 7, 2, 7, 2, 2, 2, 2, 7, 2, 3, 2, 2, 2, 2, 5, 2, 2, 5, 2, 19, 2, 2, 2, 5, 2, 2, 3, 2, 3, 2, 2, 17, 2, 5, 5, 2, 2, 2, 7, 23, 2, 2, 3, 3, 3, 5, 2, 2, 19, 2, 5, 2, 3, 2
Offset: 1
Keywords
Examples
Between p(23)=83 and p(24)=89, the relevant fixed points are {5,13,2,2,13}, of which the smallest is 2=a(24).
Programs
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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]}]; sopf[x_] := Apply[Plus, ba[x]]; Table[Min[Table[FixedPoint[sopf, w], {w, 1+Prime[n], Prime[n+1]-1}]], {n, 2, 103}]
Formula
a(n) = Min_{x=1+prime(n)..prime(n+1)-1} A075860(x).
Comments