login
Decimal expansion of prime nested prime(n)-th roots.
1

%I #28 Mar 04 2023 08:59:14

%S 1,9,0,9,0,5,8,1,1,1,4,4,1,9,2,2,0,2,6,8,8,5,8,3,1,4,2,8,5,6,2,8,1,8,

%T 8,4,9,0,2,2,2,7,2,6,0,2,6,4,3,8,9,4,1,8,4,6,6,3,2,0,1,8,6,6,4,7,2,3,

%U 8,4,6,7,9,2,1,1,9,3,7,8,4,6,1,2,4,9,1

%N Decimal expansion of prime nested prime(n)-th roots.

%H Paolo Xausa, <a href="/A343587/b343587.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Nested_radical">Nested radical</a>

%F (2 + (3 + (5 + (7 + (prime(n) + ...)^(1/prime(n)))^(1/7))^(1/5))^(1/3))^(1/2).

%e 1.90905811144192202688583142856281884902227260264389418466320186647238...

%t RealDigits[Fold[Surd[#1+#2,#2]&,0,Prime[Range[55,1,-1]]],10,200][[1]] (* _Paolo Xausa_, Mar 04 2023 *)

%o (PARI) localprec(100); N=100; my(p=prime(N), x=0); for (k=1, N, x = (x + p)^(1/p); p = precprime(p-1);); x \\ _Michel Marcus_, Apr 21 2021

%Y Cf. A000040, A105546, A296547.

%K nonn,cons

%O 1,2

%A _Paolo Xausa_, Apr 21 2021

%E More terms from _Paolo Xausa_, Mar 04 2023