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A112562 Sieve performed by successive iterations of steps where step m is: keep m terms, remove the next 4 and repeat; as m = 1,2,3,.. the remaining terms form this sequence. 4
1, 6, 31, 96, 241, 546, 1171, 1776, 2761, 5046, 7591, 11856, 19021, 20706, 31711, 44016, 60481, 71946, 92191, 120216, 138601, 181986, 226831, 302496, 379381, 400686, 487831, 574656, 704461, 831606, 1029631, 1092936, 1333321, 1462146 (list; graph; refs; listen; history; text; internal format)
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 5); thus the product will eventually reach a maximum value of a(n).

LINKS

Table of n, a(n) for n=0..33.

FORMULA

a(n) = 1 + 5*A073362(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 4, repeat; giving

1,6,11,16,21,26,31,36,41,46,51,56,61,66,...

Step 2: keep 2 terms, remove the next 4, repeat; giving

1,6,31,36,61,66,91,96,121,126,151,156,...

Step 3: keep 3 terms, remove the next 4, repeat; giving

1,6,31,96,121,126,211,216,241,306,331,...

Continuing in this way, we obtain this sequence.

Using the floor function product formula:

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

11/10]*12/11]*14/13]*15/14]*16/15]*18/17]*19/18]*20/19] = 21.

PROG

(PARI) {a(n)=local(A=n, B=0, k=0); until(A==B, k=k+1; if(k%5==0, k=k+1); B=A; A=floor(A*(k+1)/k)); 1+A}

CROSSREFS

Cf. A073362, A112560, A112561, A112563, A112564, A112565, A112566, A112567, A112568, A112569.

Sequence in context: A087725 A273790 A096959 * A244716 A024447 A143568

Adjacent sequences:  A112559 A112560 A112561 * A112563 A112564 A112565

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 14 2005

STATUS

approved

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Last modified December 9 00:44 EST 2016. Contains 278959 sequences.