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A219178
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a(n) = first unlucky number removed at the n-th stage of Lucky sieve.
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17
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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Other identities.
(End)
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(Scheme) (define (A219178 n) (A255543bi n 1)) ;; Code for A255543bi given in A255543.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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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
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STATUS
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approved
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