login
a(1)=2; for n>1, if n is in the sequence then a(n) is the smallest even integer > a(n-1), otherwise a(n) = a(n-1) + 3.
3

%I #12 May 14 2022 11:31:36

%S 2,4,7,8,11,14,16,18,21,24,26,29,32,34,37,38,41,42,45,48,50,53,56,58,

%T 61,62,65,68,70,73,76,78,81,82,85,88,90,92,95,98,100,102,105,108,110,

%U 113,116,118,121,122,125,128,130,133,136,138,141,142,145,148

%N a(1)=2; for n>1, if n is in the sequence then a(n) is the smallest even integer > a(n-1), otherwise a(n) = a(n-1) + 3.

%H Amiram Eldar, <a href="/A080704/b080704.txt">Table of n, a(n) for n = 1..10000</a>

%H Amiram Eldar, <a href="/A080704/a080704.jpg">Plot of a(n)/n for n = 10000..100000</a>

%F It seems that a(n)/n -> 2.4799.... = 62/25 ?

%t a[1] = 2; a[n_] := a[n] = Module[{s = Array[a, n-1]}, a[n-1] + If[MemberQ[s, n], If[OddQ[a[n-1]], 1, 2], 3]]; Array[a, 100] (* _Amiram Eldar_, May 14 2022 *)

%o (PARI) for(n=2,400,an[n]=if(setsearch(Set(vector(n-1,i,a(i))),n),if(a(n-1)%2,a(n-1)+1,a(n-1)+2),a(n-1)+3))

%Y Cf. A080705, A064437, A080717.

%K nonn,easy

%O 1,1

%A _Benoit Cloitre_, Mar 01 2003