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

%I A111422 #20 Feb 22 2024 13:32:54
%S A111422 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 A111422 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 A111422 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 A111422 a(n) = n-th decimal digit of the fractional part of the cube root of the n-th prime.
%D A111422 John D. Barrow, The Infinite Book, Pantheon Book New York 2005, pp. 69-76.
%e A111422 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 A111422 a[n_] := Block[{rd = RealDigits[(Prime@n)^(1/3), 10, 111]}, rd[[1, n + rd[[2]]]]];
%t A111422 Array[a, 105] (* _Robert G. Wilson v_, Nov 17 2005 *)
%o A111422 (PARI) a(n) = localprec(n+1); floor(frac(sqrtn(prime(n), 3))*10^n) % 10; \\ _Michel Marcus_, Feb 22 2024
%Y A111422 Cf. A071901.
%K A111422 easy,nonn,base
%O A111422 2,1
%A A111422 _Cino Hilliard_, Nov 13 2005
%E A111422 More terms from _Robert G. Wilson v_, Nov 17 2005