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A082370
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a(n) = number of sets of consecutive primes whose arithmetic mean is A000040(n).
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3
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1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 4, 1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 3, 1, 2, 4, 3, 3, 5, 1, 1, 6, 2, 3, 1, 2, 1, 2, 3, 2, 3, 2, 1, 1, 2, 2, 2, 4, 2, 1, 2, 4, 3, 3, 3, 2, 2, 1, 2, 1, 4, 3, 5, 2, 1, 2, 1, 3, 1, 3, 1, 3, 3, 2, 3, 2, 3, 1, 1, 2, 1, 5, 2, 1, 2, 3, 1, 2, 1, 3, 3, 2, 1, 1, 5, 2, 2
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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For n=3; A000040(3) = 5. the two sets are 5/1 = 5, (3+5+7)/3 = 5. so a(3)=2.
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MAPLE
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N:= 300:
P:= [0, seq(ithprime(i), i=1..N)]:
S:= ListTools:-PartialSums(P):
mmax:= numtheory:-pi(floor(S[N]/N)):
V:= Vector(1..mmax, 1):
for i from 1 to N+1 do
for j from i+2 to N+1 do
r:= (S[j]-S[i])/(j-i);
if r::integer and isprime(r) then
k:= numtheory:-pi(r);
if k <= mmax then
V[k]:= V[k]+1
fi
fi
od od:
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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