04-08-2015, 09:20 AM

The Programme inserts symbolics in the Sequence Aplet to reproduce the sequence

http://oeis.org/A025581

in U1 & its partial sums

http://oeis.org/A121924

in U2. The sub-programme SEQSET produces an agreeable environment in the Sequence Aplet for the necessary symbolics.

Note: I considered programming this for the Prime but was deterred by the upper limit of 40,000 for indices in the Prime Sequence App - the 38G produces exactly correct results up to 2,000,000 & beyond (I don't know the upper limit for exactly correct) & accordingly decided not to bother.

RUN SEQSET:

RECURSE(U,COMB(1+ROUND(√(2*N),0),2)-N,0,1)►U1(N):

CHECK 1:

RECURSE(U,COMB(U3(N),3)+(N-COMB(U3(N),2))*(U3(N)^2+3*U3(N)-2*N-2)/4,0,1)►U2(N):

CHECK 2:

RECURSE(U,ROUND(√(2*N+.25),0),0,0)►U3(N):

SEQSET

SELECT Sequence:

UNCHECK 0:

0►NumFont:

0►Simult:

2►Angle:

1►InvCross:

1►NumStep:

1►Format:

1►NumCol:

1►NumStart:

6►NumRow:

RECURSE(U,0,0,0)►U1(N):

Ans►U2(N):

Ans►U3(N):

Ans►U4(N):

Ans►U5(N):

Ans►U6(N):

Ans►U7(N):

Ans►U8(N):

Ans►U9(N):

Ans►U0(N):

http://oeis.org/A025581

in U1 & its partial sums

http://oeis.org/A121924

in U2. The sub-programme SEQSET produces an agreeable environment in the Sequence Aplet for the necessary symbolics.

Note: I considered programming this for the Prime but was deterred by the upper limit of 40,000 for indices in the Prime Sequence App - the 38G produces exactly correct results up to 2,000,000 & beyond (I don't know the upper limit for exactly correct) & accordingly decided not to bother.

RUN SEQSET:

RECURSE(U,COMB(1+ROUND(√(2*N),0),2)-N,0,1)►U1(N):

CHECK 1:

RECURSE(U,COMB(U3(N),3)+(N-COMB(U3(N),2))*(U3(N)^2+3*U3(N)-2*N-2)/4,0,1)►U2(N):

CHECK 2:

RECURSE(U,ROUND(√(2*N+.25),0),0,0)►U3(N):

SEQSET

SELECT Sequence:

UNCHECK 0:

0►NumFont:

0►Simult:

2►Angle:

1►InvCross:

1►NumStep:

1►Format:

1►NumCol:

1►NumStart:

6►NumRow:

RECURSE(U,0,0,0)►U1(N):

Ans►U2(N):

Ans►U3(N):

Ans►U4(N):

Ans►U5(N):

Ans►U6(N):

Ans►U7(N):

Ans►U8(N):

Ans►U9(N):

Ans►U0(N):