A111422 a(n) = n-th decimal digit of the fractional part of the cube root of the n-th prime.

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, 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, 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

Offset: 2

Author

Cino Hilliard, Nov 13 2005

Keywords

• easy
• nonn
• base

Examples

			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.
		

References

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

Crossrefs

Cf. A071901.

Programs

Mathematica

a[n_] := Block[{rd = RealDigits[(Prime@n)^(1/3), 10, 111]}, rd[[1, n + rd[[2]]]]];
Array[a, 105] (* Robert G. Wilson v, Nov 17 2005 *)

PARI

a(n) = localprec(n+1); floor(frac(sqrtn(prime(n), 3))*10^n) % 10; \\ Michel Marcus, Feb 22 2024

Extensions

More terms from Robert G. Wilson v, Nov 17 2005