A219178 a(n) = first unlucky number removed at the n-th stage of Lucky sieve.

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

Offset: 1

Author

Phil Carmody, Nov 15 2012

Keywords

• nonn
• easy

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

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..333
• Wikipedia, Lucky Number

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.

Programs

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 *)

Scheme

(define (A219178 n) (A255543bi n 1)) ;; Code for A255543bi given in A255543.

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)

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