cp's OEIS Frontend

A236399 Left factorial !p, where p = prime(n).

%I A236399 #22 Nov 06 2024 04:11:27
%S A236399 2,4,34,874,4037914,522956314,22324392524314,6780385526348314,
%T A236399 1177652997443428940314,316196664211373618851684940314,
%U A236399 274410818470142134209703780940314,382630662501032184766604355445682020940314,836850334330315506193242641144055892504420940314
%N A236399 Left factorial !p, where p = prime(n).
%H A236399 G. C. Greubel, <a href="/A236399/b236399.txt">Table of n, a(n) for n = 1..87</a>
%H A236399 Romeo Mestrovic, <a href="http://arxiv.org/abs/1312.7037">Variations of Kurepa's left factorial hypothesis</a>, arXiv:1312.7037 [math.NT], 2013.
%F A236399 a(n) = Sum_{k=0..prime(n)-1} k!. - _G. C. Greubel_, Mar 29 2019
%p A236399 lf:=n->add(k!,k=0..n-1);
%p A236399 [seq(lf(ithprime(n)),n=1..30)];
%p A236399 # 2nd program:
%p A236399 A236399 := proc(n)
%p A236399     A003422(ithprime(n)) ;
%p A236399 end proc:
%p A236399 seq(A236399(n),n=1..5) ; # _R. J. Mathar_, Dec 19 2016
%t A236399 leftFac[n_] := Sum[k!, {k, 0, n - 1}];
%t A236399 a[n_] := leftFac[Prime[n]];
%t A236399 Array[a, 13] (* _Jean-François Alcover_, Nov 24 2017 *)
%o A236399 (PARI) vector(15, n, sum(k=0,prime(n)-1, k!)) \\ _G. C. Greubel_, Mar 29 2019
%o A236399 (Magma) [(&+[Factorial(k): k in [0..(NthPrime(n)-1)]]): n in [1..15]]; // _G. C. Greubel_, Mar 29 2019
%o A236399 (Sage) [sum(factorial(k) for k in (0..(nth_prime(n)-1))) for n in (1..15)] # _G. C. Greubel_, Mar 29 2019
%Y A236399 A subsequence of A003422.
%K A236399 nonn,easy
%O A236399 1,1
%A A236399 _N. J. A. Sloane_, Jan 29 2014