[VA] SRC #017 - April 1st, 2024 Spring Special

[Gerson W. Barbosa]

LOL the First

HP-75C program:

10 OPTION BASE 0
15 INTEGER I,J,N
20 N=5
25 B=1000000
30 DIM A(9),B(5),C(12)
35 REM DIM A(N+4), B(N), C(2*N+2); N>1
40 FOR I=0 TO 2*N+2 @ C(I)=0 @ NEXT I
45 FOR I=0 TO N+4 @ A(I)=0 @ NEXT I
50 FOR I=1 TO N
55 READ A(I)
60 B(I)=A(I)
65 NEXT I
70 FOR I=N TO 1 STEP -1
75 T1=0 @ A1=0
80 FOR J=N-I+4 TO -1 STEP -1
85 C2=(T1+B(I)*A(J+1))/B
90 A1=FP(C2)*B
95 C(I+J)=C(I+J)+A1
100 T1=IP(C2)
105 NEXT J
110 NEXT I
115 FOR I=2*N TO 2 STEP -1
120 T=C(I)/B
125 C(I)=FP(T)*B
130 C(I-1)=C(I-1)+IP(T)
135 NEXT I
140 FOR I=0 TO 2*N-1
145 DISP C(I);
150 NEXT I
155 END
160 DATA 141422,82876,67219,949805,50005

>RUN
20000 205525 5225 202000 505202 222520 222202 205205 550 500025

That is,

141422082876067219949805050005^2 =

20000205525005225202000505202222520222202205205000550500025


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LOL the Fifth:

I have digressed on this one and haven't done what has been asked (No cigar, I guess :-). I'll just say the fractional part tends to 1 minus a known mathematical constant to which the following is a pandigital appoximation in RPL algebraic expression format, good to twelve digits:

'INV(√(3+7/((29/10)^8-INV(SQ((4^5)^INV(6))))))'

On the HP 50g in approximate mode, '1 - INV(√(3+7/((29/10)^8-INV(SQ((4^5)^INV(6))))))' should return the same numeric result as '1+Psi(1)'.

Edited to fix a typo