A082431 -id:A082431 - cp's OEIS frontend

A050237 a(n) = the smallest number m such that there are exactly n sets of consecutive primes, each of which has an arithmetic mean of m.

1, 2, 5, 12, 38, 30, 173, 165, 12259, 8803, 36735, 67263, 5296771, 32975, 1147233

Offset: 0

Naohiro Nomoto, May 08 2003

First appearance of n in A122821.

			a(4) = 38 because there are exactly four sets of consecutive primes which have means of 38: {31,37,41,43}, {29,...,47}, {23,...,53} and {2,...,83},

Cf. A060863, A082431, A122821.

{a(n)= m=2; starting_index=1; k=starting_index; sum_of_primes=0; prime_count=0; sets=0; until( (prime(starting_index)>m) && (sets==n), if( (prime(starting_index)> m) || (sets>n), m++; sets=0; starting_index=1; k=starting_index); sum_of_primes=sum_of_primes+prime(k); prime_count++; mean=sum_of_primes/ prime_count; if(meanRick L. Shepherd, Jun 14 2004

Edited by Don Reble, Jun 17 2003

A082370 a(n) = number of sets of consecutive primes whose arithmetic mean is A000040(n).

Original entry on oeis.org

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

Offset: 1

Naohiro Nomoto, May 11 2003

			For n=3; A000040(3) = 5. the two sets are 5/1 = 5, (3+5+7)/3 = 5. so a(3)=2.

Robert Israel, Table of n, a(n) for n = 1..4000

Cf. A050221, A060863, A082431, A122821.

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:
convert(V,list); # Robert Israel, Mar 18 2018

a(n) = A122821(A000040(n)).

Extended by Ray Chandler, Oct 03 2006

cp's OEIS Frontend

A050237 a(n) = the smallest number m such that there are exactly n sets of consecutive primes, each of which has an arithmetic mean of m.

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