0,2

Formula: a(n) = 1 + [...[[[[n*2/1]3/2]5/4]6/5]...(k+1)/k]... where denominators k of the fractions used in the product vary over all natural numbers not congruent to 0 (mod 3); thus the product will eventually reach a maximum value of a(n).

a(n) = 1 + 3*A073360(n).

Sieve starts with the natural numbers:

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15...

Step 1: keep 1 term, remove the next 2, repeat; giving

1,4,7,10,13,16,19,22,25,28,31,34,37,40,...

Step 2: keep 2 terms, remove the next 2, repeat; giving

1,4,13,16,25,28,37,40,49,52,61,64,73,76,...

Step 3: keep 3 terms, remove the next 2, repeat; giving

1,4,13,28,37,40,61,64,73,88,97,100,121,...

Continuing in this way, we obtain this sequence.

Using the floor function product formula:

a(2)=1+[[[[[[[(2)*2/1]3/2]5/4]6/5]8/7]9/8]11/10]12/11]=13.

(PARI) {a(n)=local(A=n, B=0, k=0); until(A==B, k=k+1; if(k%3==0, k=k+1); B=A; A=floor(A*(k+1)/k)); 1+A}

Cf. A073360, A112561, A112562, A112563, A112564, A112565, A112566, A112567, A112568, A112569.

Sequence in context: A060488 A054968 A087035 this_sequence A009561 A155266 A155413

Adjacent sequences: A112557 A112558 A112559 this_sequence A112561 A112562 A112563

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Oct 14 2005