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 A306834 Numerator of the barycenter of first n primes defined as a(n) = numerator(Sum_{i=1..n} (i*prime(i)) / Sum_{i=1..n} prime(i)). 4
 1, 8, 23, 3, 53, 184, 303, 65, 331, 952, 1293, 1737, 1135, 2872, 3577, 1475, 1357, 6526, 7799, 3073, 1344, 12490, 14399, 16535, 948, 502, 24367, 9121, 7631, 33914, 37851, 42043, 1663, 51290, 56505, 20647, 33875, 73944, 80457, 87377, 47358, 34106, 1033, 119023, 31972, 137042, 146959, 157663 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It appears that lim_{n->infinity} (1/n)*(A014285(n)/A007504(n)) = k, where k is a constant around 2/3. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = numerator(Sum_{i=1..n} (i*prime(i)) / Sum_{i=1..n} prime(i)). a(n) = numerator(A014285(n)/A007504(n)). MAPLE N:= 100: # for a(1)..a(N) Primes:= map(ithprime, [\$1..N]): S1:= ListTools:-PartialSums(Primes): S2:= ListTools:-PartialSums(zip(`*`, Primes, [\$1..N])): map(numer, zip(`/`, S2, S1)); # Robert Israel, Apr 07 2019 MATHEMATICA a[n_]:=Sum[i*Prime[i], {i, 1, n}]/Sum[Prime[i], {i, 1, n}]; Table[a[n]//Numerator, {n, 1, 40}] PROG (PARI) a(n) = numerator(sum(i=1, n, i*prime(i))/sum(i=1, n, prime(i))); \\ Michel Marcus, Mar 15 2019 CROSSREFS Cf. A272206, A007504, A014285. Sequence in context: A117613 A215740 A304177 * A109271 A029755 A022420 Adjacent sequences: A306831 A306832 A306833 * A306835 A306836 A306837 KEYWORD nonn,frac,look AUTHOR Andres Cicuttin, Mar 12 2019 STATUS approved

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Last modified September 8 01:34 EDT 2024. Contains 375749 sequences. (Running on oeis4.)