login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002960 The square sieve.
(Formerly M1346)
3
2, 5, 8, 12, 17, 22, 28, 34, 41, 48, 56, 65, 74, 84, 94, 105, 116, 128, 140, 153, 166, 180, 194, 209, 224, 240, 257, 274, 292, 310, 329, 348, 368, 388, 409, 430, 452, 474, 497, 520, 544, 568, 593, 618, 644, 670, 697, 724, 752, 780, 809, 838, 868, 898, 929, 960, 992, 1025, 1058, 1092, 1126, 1161, 1196 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See example for the construction used.

Conjecture: The first differences are given by A274089 (omitting the first two terms 1 and 2). - Alisa Ediger, Jun 04 2016

REFERENCES

David L. Silverman, Problem #116, The Square Sieve, J. Rec. Math., 4 (1971), 288-289.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Index entries for sequences generated by sieves

FORMULA

Conjecture: a(n) = a(n-1) + 1 + floor(sqrt(a(n-1) + 1 + floor(sqrt(a(n-1))))); a(1) = 2. - Gionata Neri, Jun 22 2015

Conjecture: a(n) = 2^(x-1)*(2^(x-1)+y-1) + floor((y+1)^2/4), where y = n+1+x-2^x and x = floor(log_2(n+1+floor(log_2(n)))). - Gionata Neri, Jul 05 2015

EXAMPLE

Start with

  1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,...

Remove all square-th elements, 1,4,9,16,... to get

  2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,...

Return 2 is the first element in the sequence and remove it

  3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,...

Remove the 1,4,9,16th,... elements

  5,6,8,10,11,12,14,15,17,18,19,20,22,23,...

Return 5 as the next element in the sequence and remove it

  6,8,10,11,12,14,15,17,18,19,20,22,23,...

Remove the 1,4,9,16th,... elements

  8,10,12,14,15,17,19,20,22,23,...

Return 8 as the next element in the sequence and remove it

  10,12,14,15,17,19,20,22,23,...

Remove the 1,4,9,16th,... elements

  12,14,15,19,20,22,23,...

etc. - Sean A. Irvine, Dec 10 2014

MAPLE

sieve:= L -> subsop(seq(i^2=NULL, i=1..floor(sqrt(nops(L)))), L):

A:= [$1..10^5]:

for n from 1 do

  A:= sieve(A);

  if nops(A) = 0 then break fi;

  R[n]:= A[1];

  A:= subsop(1=NULL, A);

od:

seq(R[i], i=1..n-1); # Robert Israel, Dec 11 2014

MATHEMATICA

First /@ NestWhileList[Function[w, {First@ #, Rest@ #} &@ Delete[Last@ w, #] &@ Map[{#} &, Reverse@ Range[Floor@ Sqrt@ Length[Last@ w]]^2]], {0, Range@ 1200}, Length@ Last@ # > 1 &] (* Michael De Vlieger, Jun 05 2016 *)

CROSSREFS

Cf A274089.

Sequence in context: A330188 A214047 A241566 * A022942 A183861 A024534

Adjacent sequences:  A002957 A002958 A002959 * A002961 A002962 A002963

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

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 August 3 20:04 EDT 2020. Contains 336201 sequences. (Running on oeis4.)