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Merge digits of Pi and Phi (golden section) starting with 3.
1

%I #19 Aug 22 2024 20:42:44

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

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

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

%N Merge digits of Pi and Phi (golden section) starting with 3.

%C Is the real number 3.611381... irrational? Transcendental?

%e Pi = 3, 1, 4, 1, 5, 9, 2, ...

%e Phi = 6, 1, 8, 0, 3, 3, 9, ...

%e so we get 3, 6, 1, 1, 4, 8, 1, ... [corrected by _Jesse Fiedler_, Aug 22 2019]

%t Riffle[ RealDigits[ Pi, 10, 55][[1]], RealDigits[ GoldenRatio - 1, 10, 55][[1]], 2] (* _Robert G. Wilson v_, Mar 19 2014 *)

%o (PARI) \\ piphi alternating between Pi and Phi digit sequence

%o \\ piphi.gp Pi and phi digits merged

%o { piphi(n) = default(realprecision,10000); p = Pi/10; e = (sqrt(5)-1)/2; default(realprecision,28); forstep(x=1,n,2, d = p*10; d1=floor(d); p = frac(d); d2 = e*10; d3 = floor(d2); e = frac(d2); print1(d1" "d3" "); ); }

%Y Cf. A058382.

%K base,cons,nonn

%O 1,1

%A _Cino Hilliard_, Nov 16 2002

%E More terms from _Robert G. Wilson v_, Mar 19 2014

%E Offset changed by _Alois P. Heinz_, Aug 22 2024