A111421 a(n) = n-th decimal digit + 1 of the fractional part formed by the square root of the n-th prime.

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

Offset: 2

Author

Cino Hilliard, Nov 12 2005

Keywords

• easy
• nonn
• base

Comments

Also a Cantor diagonal proving the irrational numbers are a non-denumerable infinite set. Also A071901(n)+ 1.

Examples

			The 2nd prime is 3. Sqrt(3) = 1.7320508..., The 2nd entry after the decimal point is 3 and 3+1=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

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

PARI

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

Extensions

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