A343587 Decimal expansion of prime nested prime(n)-th roots.
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, 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, 8, 4, 6, 7, 9, 2, 1, 1, 9, 3, 7, 8, 4, 6, 1, 2, 4, 9, 1
Offset: 1
Examples
1.90905811144192202688583142856281884902227260264389418466320186647238...
Links
- Paolo Xausa, Table of n, a(n) for n = 1..10000
- Wikipedia, Nested radical
Programs
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Mathematica
RealDigits[Fold[Surd[#1+#2,#2]&,0,Prime[Range[55,1,-1]]],10,200][[1]] (* Paolo Xausa, Mar 04 2023 *)
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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
Formula
(2 + (3 + (5 + (7 + (prime(n) + ...)^(1/prime(n)))^(1/7))^(1/5))^(1/3))^(1/2).
Extensions
More terms from Paolo Xausa, Mar 04 2023