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%I #14 Feb 22 2024 15:12:43
%S 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,
%T 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,
%U 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
%N a(n) = n-th decimal digit + 1 of the fractional part formed by the square root of the n-th prime.
%C Also a Cantor diagonal proving the irrational numbers are a non-denumerable infinite set. Also A071901(n)+ 1.
%D John D. Barrow, The Infinite Book, Pantheon Book New York 2005, pp. 69-76.
%e 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.
%t 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 *)
%o (PARI) a(n) = localprec(n+1); (floor(frac(sqrt(prime(n)))*10^n)+1) % 10; \\ _Michel Marcus_, Feb 22 2024
%Y Cf. A071901.
%K easy,nonn,base
%O 2,1
%A _Cino Hilliard_, Nov 12 2005
%E More terms from _Robert G. Wilson v_, Nov 17 2005