

A219178


a(n) = first unlucky number removed at the nth 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
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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

Antti Karttunen, Table of n, a(n) for n = 1..333
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}] (* JeanFrançois 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).
Cf. A000959, A001248, A254100, A255549, A255550, A255553.
Sequence in context: A215426 A215277 A027714 * A184868 A077317 A092946
Adjacent sequences: A219175 A219176 A219177 * A219179 A219180 A219181


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



