%I #20 Feb 22 2024 13:32:54

%S 2,4,9,9,8,4,5,4,9,6,9,5,7,2,4,0,4,5,0,0,6,3,7,8,4,6,7,9,3,6,7,7,8,2,

%T 5,9,0,6,1,8,8,8,3,9,1,6,6,9,9,9,4,4,3,7,7,2,4,4,7,6,7,1,8,4,6,6,9,0,

%U 6,5,7,9,8,9,7,5,2,4,5,1,7,0,9,4,7,0,6,3,1,7,3,9,3,7,0,9,4,0,9,7,0,9,7,2,0

%N a(n) = n-th decimal digit of the fractional part of the cube root of the n-th prime.

%D John D. Barrow, The Infinite Book, Pantheon Book New York 2005, pp. 69-76.

%e The 2nd prime is 3. 3^(1/3) = 1.442249..., The 2nd entry after the decimal point is 4 the 2nd entry in the table.

%t a[n_] := Block[{rd = RealDigits[(Prime@n)^(1/3), 10, 111]}, rd[[1, n + rd[[2]]]]];

%t Array[a, 105] (* _Robert G. Wilson v_, Nov 17 2005 *)

%o (PARI) a(n) = localprec(n+1); floor(frac(sqrtn(prime(n), 3))*10^n) % 10; \\ _Michel Marcus_, Feb 22 2024

%Y Cf. A071901.

%K easy,nonn,base

%O 2,1

%A _Cino Hilliard_, Nov 13 2005

%E More terms from _Robert G. Wilson v_, Nov 17 2005