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

Author

Paolo Xausa, Apr 21 2021

Keywords

• nonn
• cons

Examples

			1.90905811144192202688583142856281884902227260264389418466320186647238...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Nested radical

Crossrefs

Cf. A000040, A105546, A296547.

Programs

Mathematica

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

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