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A219178 a(n) = first unlucky number removed at the n-th stage of Lucky sieve. 17
2, 5, 19, 27, 45, 55, 85, 109, 139, 157, 175, 213, 255, 265, 337, 363, 387, 411, 423, 457, 513, 547, 597, 637, 675, 715, 789, 807, 843, 871, 907, 987, 1033, 1083, 1113, 1125, 1267, 1297, 1315, 1371, 1407, 1465, 1515, 1555, 1609, 1651, 1671, 1707, 1851, 1873, 1927, 1969 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
First numbers removed by each lucky number in the lucky number sieve. - This is the original definition of the sequence, still valid from a(2) onward.
a(1) = 2, because at the first stage of Lucky sieve, all even numbers are removed, of which 2 is the first one. - Antti Karttunen, Feb 26 2015
LINKS
Wikipedia, Lucky Number
FORMULA
From Antti Karttunen, Feb 26 2015: (Start)
a(n) = A255543(n,1).
Other identities.
For all n >= 2, a(n) = A255553(A001248(n)).
(End)
EXAMPLE
1 and 2 are a special case in the lucky number sieve, (1 is the lucky number, but every 2nd element is removed) so are ignored [in the original version of the sequence, which started from a(2). Now we have a(1) = 2. - Antti Karttunen, Feb 26 2015]. The 2nd lucky number, 3, removes { 5, 11, ... } from the list, so a(2) = 5. The 3rd lucky number, 7, removes { 19, 39, ... } from the list, so a(3)=19.
MATHEMATICA
rows = 52; cols = 1; L = 2 Range[0, 10^4] + 1; A = Join[{2 Range[cols]}, Reap[For[n = 2, n <= rows, r = L[[n++]]; L0 = L; L = ReplacePart[L, Table[r i -> Nothing, {i, 1, Length[L]/r}]]; Sow[Complement[L0, L][[1 ;; cols]]]]][[2, 1]]]; Table[A[[n, 1]], {n, 1, rows}] (* Jean-François Alcover, Mar 15 2016 *)
PROG
(Scheme) (define (A219178 n) (A255543bi n 1)) ;; Code for A255543bi given in A255543.
CROSSREFS
Column 1 of A255543, Column 2 of A255545 (And apart from the first term, also column 2 of A255551).
Sequence in context: A215426 A215277 A027714 * A184868 A077317 A092946
KEYWORD
nonn,easy
AUTHOR
Phil Carmody, Nov 15 2012
EXTENSIONS
Term a(1) = 2 prepended, without changing the rest of sequence. Name changed, with the original, more restrictive definition moved to the Comments section. - Antti Karttunen, Feb 26 2015
STATUS
approved

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Last modified May 23 05:59 EDT 2024. Contains 372758 sequences. (Running on oeis4.)