

A184939


From the base sequence of the positive integers, keep the first two, remove the next three, keep the next five, remove the next seven, ..., block lengths determined by the prime numbers.


1



1, 2, 6, 7, 8, 9, 10, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 130, 131, 132
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OFFSET

1,2


COMMENTS

Accept 1st prime, reject 2nd prime, accept 3rd prime, reject 4th prime, ... starting with natural numbers A000027. First string of consecutive values ends with 2, second such string ends with 10 = 2+3+5, 3rd such string ends with 28 = 2+3+5+7+11, namely A007504(2k+1).


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000


EXAMPLE

In parentheses the blocks of integers removed: 1 2 (3 4 5) 6 7 8 9 10 (11 12 13 14 15 16 17) 18 19 20 21 22 23 24 25 26 27 28 (29 30 ...).


MAPLE

L := [] ; p := 2 ; ptr := 1 ;
while p < 40 do
L := [op(L), seq(j, j=ptr..ptr+p1)] ; ptr := ptr+p ; p := nextprime(p) ;
ptr := ptr+p ; p := nextprime(p) ;
end do:
L ; # R. J. Mathar, Feb 08 2011


MATHEMATICA

Module[{nn=20, t}, t=Total[Prime[Range[nn]]]; Take[TakeList[Range[t], Prime[ Range[nn]]], {1, nn, 2}]]//Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 04 2019 *)


CROSSREFS

Cf. A000040, A004201, A007504.
Sequence in context: A073005 A091942 A047555 * A043050 A159843 A243652
Adjacent sequences: A184936 A184937 A184938 * A184940 A184941 A184942


KEYWORD

nonn,easy


AUTHOR

Jonathan Vos Post, Feb 02 2011


STATUS

approved



