A343623
E.g.f.: -log(1 - x - Sum_{k>=2} prime(k-1) * x^k / k!).
Original entry on oeis.org
1, 3, 11, 59, 416, 3683, 39093, 484220, 6854176, 109150227, 1931303809, 37589753206, 798135918850, 18358887315769, 454779141016707, 12070296596154136, 341715021307029876, 10278722402921420619, 327369178071821161755, 11005696560250745851048, 389469699942038630639524
Offset: 1
-
nmax = 21; CoefficientList[Series[-Log[1 - x - Sum[Prime[k - 1] x^k/k!, {k, 2, nmax}]], {x, 0, nmax}], x] Range[0, nmax]! // Rest
A353155
Logarithmic transform of odd primes.
Original entry on oeis.org
3, -4, 16, -94, 740, -7322, 87096, -1209242, 19190176, -342623408, 6797028096, -148325493672, 3531032617412, -91064679012376, 2529198638215228, -75262590212948118, 2388933783463085676, -80567150574145456164, 2876970976034496438802, -108441134639989639371264
Offset: 1
-
a:= proc(n) option remember; (t-> `if`(n=0, 0, t(n) -add(j*
binomial(n, j)*t(n-j)*a(j), j=1..n-1)/n))(i->ithprime(i+1))
end:
seq(a(n), n=1..25); # Alois P. Heinz, Apr 27 2022
-
nmax = 20; CoefficientList[Series[Log[1 + Sum[Prime[k + 1] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]! // Rest
a[n_] := a[n] = Prime[n + 1] - (1/n) Sum[Binomial[n, k] Prime[n - k + 1] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 1, 20}]
Showing 1-2 of 2 results.