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
Keywords
Examples
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.
Crossrefs
Programs
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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}
Formula
a(n) = 1 + 6*A073363(n).
Comments