cp's OEIS Frontend

A339764 Decimal expansion of Varona's constant = Sum_{k >= 1} prime(k)/2^(k + k!).

%I A339764 #27 Jan 14 2023 13:36:57
%S A339764 6,9,7,2,6,5,6,5,1,0,7,7,0,3,2,0,8,9,2,3,3,3,9,8,4,3,7,5,0,0,0,0,0,0,
%T A339764 0,0,2,5,8,6,0,8,7,5,7,1,8,0,9,0,3,2,5,1,7,5,3,1,2,2,0,3,8,1,8,8,8,9,
%U A339764 4,0,4,9,1,2,0,1,0,6,4,2,2,4,8,9,8,5,9,2,5,4,7,3,1,9,2,5,3,7,5,3,8,1,2,5,1,7,9,7,0,8,0,0,3,9,9,7,8,0,2,7,3,4,3,7,5,0,0,0,0,0,0
%N A339764 Decimal expansion of Varona's constant = Sum_{k >= 1} prime(k)/2^(k + k!).
%C A339764 Varona's constant v is transcendental and generates the primes via prime(1)=2=floor(4*v) and for n>1 prime(n) = floor(v*2^(n+n!)) - 2^(1+n!-(n-1)!)*floor(v*2^(n-1+(n-1)!)).
%H A339764 Juan L. Varona, <a href="https://arxiv.org/abs/2012.11750">A couple of transcendental prime-representing constants</a>, arXiv:2012.11750 [math.NT], 2020.
%H A339764 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A339764 0.69726565107703208923339843750000000025860875718090325175312203818889
%t A339764 First@RealDigits@N[Sum[Prime[i]/2^(i + i!), {i, 1, 12}], 300]
%o A339764 (PARI) suminf(k=1, prime(k)/2^(k + k!)) \\ _Michel Marcus_, Dec 21 2020
%Y A339764 Cf. A249270, A016104, A051021.
%K A339764 nonn,cons
%O A339764 0,1
%A A339764 _José María Grau Ribas_, Dec 20 2020