cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A095137 Absolute difference between the product of the first floor(n/2) even-indexed primes and the product of the first floor(n/2) odd-indexed primes.

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%I A095137 #13 Jan 11 2023 19:47:08
%S A095137 2,1,7,11,89,163,1597,3317,37823,107413,1182887,4232341,49100059,
%T A095137 184657283,2329965377,10114830259,138903895201,622143222539,
%U A095137 9382665690241,44778520855589,686482057860331,3598441529151191
%N A095137 Absolute difference between the product of the first floor(n/2) even-indexed primes and the product of the first floor(n/2) odd-indexed primes.
%F A095137 The absolute difference of Product_{j=1..floor(n/2)} p_(2j) (A066206) and Product_{k=1..floor(n/2)} p_(2j-1) (A066205).
%e A095137 a(5) = 2*5*11 - 3*7 = 89, a(6) = 3*7*13 - 2*5*11 = 163;
%e A095137 a(7) = 2*5*11*17 - 3*7*13 = 1597, a(8) = 3*7*13*19 - 2*5*11*17 = 3317.
%t A095137 PrimeFactors[n_] := Flatten[ Table[ #[[1]], {1} ] & /@ FactorInteger[n]]; f[n_] := Abs[ Product[ Prime[i], {i, 2, n, 2}] + Product[ Prime[i], {i, 1, n, 2}]]; f[1] = 2; Table[ f[n], {n, 24}]
%t A095137 Join[{2},Table[Abs[Times@@Prime[Range[1,Floor[n/2],2]]-Times@@Prime[Range[ 2,Floor[ n/2 ],2]]],{n,4,45,2}]] (* _Harvey P. Dale_, Jan 11 2023 *)
%Y A095137 Cf. A095134, A000040, A066206, A066205.
%K A095137 nonn
%O A095137 1,1
%A A095137 _Robert G. Wilson v_, May 28 2004