cp's OEIS Frontend

A215974 Numbers n such that Sum_{k=1..n} k!/2^k is an integer.

%I A215974 #29 Apr 04 2019 21:33:13
%S A215974 0,2,5,12,14,25,29,54,60,62,3445,108995,3625182,13951972,28010901,
%T A215974 7165572247,14335792539,114636743486,229264368709,458534096494
%N A215974 Numbers n such that Sum_{k=1..n} k!/2^k is an integer.
%C A215974 This sequence lists the indices n for which A215976(n)=0 (power of 2 in denominator) and for which A215990 (numerator of the sum) may be even.
%H A215974 B. M. M. de Weger, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;5a41ecf9.1208">Sums with factorials</a>, NMBRTHRY list, Aug 28 2012
%F A215974 A215974(n) = A215972(n)-1 for all n. (The two sequences differ only in the use of the upper limit. The present convention seems more natural, the other one was used in the post on the NmbrThry list.)
%e A215974 a(1)=0 is in the sequence because sum(..., 1 <= k <= 0)=0 (empty sum) is an integer.
%e A215974 1 is not in the sequence because 1!/2^1 = 1/2 is not an integer.
%e A215974 a(2)=2 is in the sequence because 1!/2^1 + 2!/2^2 = 1 is an integer.
%t A215974 sum = 0; Select[Range[0, 10^4], IntegerQ[sum += #!/2^#] &] (* _Robert Price_, Apr 04 2019 *)
%o A215974 (PARI) is_A215974(n)=denominator(sum(k=1,n,k!/2^k))==1
%o A215974 (PARI) s=0;for(k=1,9e9,denominator(s+=k!/2^k)==1&print1(k,","))
%Y A215974 Cf. A215972, A216056.
%K A215974 nonn,more
%O A215974 1,2
%A A215974 _M. F. Hasler_, Aug 29 2012
%E A215974 Terms through a(20) from Aart Blokhuis and Benne de Weger, Aug 30 2012, who thank Jan Willem Knopper for efficient programming. - _N. J. A. Sloane_, Aug 30 2012