login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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}] (* Jean-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 24 05:21 EDT 2019. Contains 325290 sequences. (Running on oeis4.)