(35S) OEIS A137442: N^2 THEN SMALLEST NOT YET LISTED & SUM

[Gerald H]

Sequence of square then smallest integer not yet listed starting at 1^2, OEIS A137442

1, 2, 4, 3, 9, 5, 16, 6, 25, 7, 36, 8, 49, 10, 64, 11, 81, 12, 100, 13, 121, 14, 144, 15, 169, 17, 196, 18, 225, 19, 256, 20, 289, 21, 324, 22, 361, 23, 400, 24, 441, 26, 484, 27, 529…..

For index N solve the equation

G = RMDR( N , 2 ) ► R * SQ( ( N + 1 ) / 2 ) + ( 1 – R ) * ( N / 2 + IP( SQRT( N / 2 ) + 0.5 ) ) + 0 * ( ( IDIV( N , 2 ) ► F + R ) ► T * ( 1 + T * ( 3 + 2 * T ) ) / 6 + ( F + IP( SQRT( F ) + 0.5 ) ► Q ) * ( Q + 1 ) / 2 – ( IP( SQRT( Q ) ) ► U ) * ( U + 1 ) * ( U + 0.5 ) / 3 ► S )

for G. You will be prompted for values other than N, ignore these prompts with R/S.

For input

N = 818

The calculator returns

G = 429

Additionally the sum (OEIS A167390) of the first 818 terms is stored in S,

S = 22,979,050