A112563 Sieve performed by successive iterations of steps where step m is: keep m terms, remove the next 5 and repeat; as m = 1,2,3,.. the remaining terms form this sequence.

1, 7, 43, 169, 505, 1051, 2527, 5083, 7729, 11635, 22681, 33937, 55483, 90889, 132595, 152251, 238057, 327643, 451249, 543355, 776161, 997927, 1258993, 1441609, 1924315, 2397571, 3221737, 4036033, 4900399, 5438665, 6691651

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..30.

Formula

a(n) = 1 + 6*A073363(n).

Example

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 5, repeat; giving
1,7,13,19,25,31,37,43,49,55,61,67,73,79,...
Step 2: keep 2 terms, remove the next 5, repeat; giving
1,7,43,49,85,91,127,133,169,175,211,217,...
Step 3: keep 3 terms, remove the next 5, repeat; giving
1,7,43,169,175,211,337,343,379,505,511,547,...
Continuing in this way, we obtain this sequence.
Using the floor function product formula:
a(2) = 1+[..[(2)*2/1]*3/2]*4/3]*5/4]*7/6]*8/7]*9/8]*10/9]*
12/11]*13/12]*14/13]*15/14]*17/16]*18/17]*19/18]*20/19]*
22/21]*23/22]*24/23]*25/24]*27/26]*28/27]*29/28]*30/29] =43.

Prog

(PARI) {a(n)=local(A=n, B=0, k=0); until(A==B, k=k+1; if(k%6==0, k=k+1); B=A; A=floor(A*(k+1)/k)); 1+A}

Crossrefs

Cf. A073363, A112560, A112561, A112562, A112564, A112565, A112566, A112567, A112568, A112569.

Sequence in context: A365302 A255314 A166813 * A143569 A351936 A193697

Adjacent sequences: A112560 A112561 A112562 * A112564 A112565 A112566

Keyword

nonn

Author

Paul D. Hanna, Oct 14 2005

Status

approved