A193732 Connell-like sequence.

1, 3, 4, 6, 8, 9, 11, 13, 15, 17, 18, 20, 22, 24, 26, 28, 30, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 110, 112, 114, 116, 118, 120

Offset: 1

Author

Ctibor O. Zizka, Aug 08 2011

Keywords

• nonn
• easy

Examples

			Let prime(n) denote the n-th prime.
Because prime(1)=2, take first 2 odd numbers giving a(1)=1, a(2)=3.
Because prime(2)=3, take 3 even numbers starting with 4 giving a(3)=4, a(4)=6, a(5)=8.
Because prime(3)=5, take 5 odd numbers starting with 9 giving a(6)=9, a(7)=11, a(8)=13, a(9)=15, a(10)=17.
Because prime(4)=7, take 7 even numbers starting with 18 gives a(11)=18, a(12)=20, ..., a(17)=30 etc.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001614.

Programs

Maple

cp:=2:ct:=1:a := proc(n) option remember: global cp,ct: if(n=1)then return 1: elif(ct=cp)then ct:=1:cp:=nextprime(cp): return a(n-1)+1: else ct:=ct+1: return a(n-1)+2: fi: end: seq(a(n),n=1..100); # Nathaniel Johnston, Aug 11 2011

Mathematica

nxt[{p_,a_}]:={NextPrime[p],Range[Last[a]+1,Last[a]+2*NextPrime[p],2]}; Transpose[NestList[nxt,{2,{1,3}},10]][[2]]//Flatten (* Harvey P. Dale, Mar 23 2016 *)