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, 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

Offset: 1

Author

Jonathan Vos Post, Feb 02 2011

Keywords

• nonn
• easy

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).

Examples

			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 ...).
		

Links

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

Crossrefs

Cf. A000040, A004201, A007504.

Programs

Maple

L := [] ; p := 2 ; ptr := 1 ;
while p < 40 do
        L := [op(L),seq(j,j=ptr..ptr+p-1)] ; 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 *)