

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



FORMULA

Other identities.
(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



KEYWORD

nonn,easy


AUTHOR



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



