A274425 Consider van Eck's sequences with a(1)=n and a(2)=0. Sequence lists the index of second occurrence of n.

4, 6, 21, 18, 13, 11, 67, 48, 25, 149, 45, 174, 122, 31, 36, 139, 42, 64, 90, 57, 106, 325, 102, 216, 111, 258, 143, 321, 226, 472, 73, 60, 82, 184, 540, 135, 93, 264, 169, 130, 549, 53, 200, 180, 229, 99, 298, 622, 671, 358, 157, 117, 1487, 476, 1478, 85, 513

Offset: 1

Author

Paolo P. Lava, Jul 13 2016

Keywords

• nonn
• easy

Examples

			Starting with a(1)=1 and a(2)=0 the second occurrence of 1 is for a(4):
1, 0, 0, 1, 3, 0, 3, 2, 0, 3, 3, 1, 8, 0, 5, 0, 2, 9, 0, 3, 9, 3, 2, ...
Starting with a(1)=2 and a(2)=0 the second occurrence of 2 is for a(6):
2, 0, 0, 1, 0, 2, 5, 0, 3, 0, 2, 5, 5, 1, 10, 0, 6, 0, 2, 8, 0, 3, 13, ...
Starting with a(1)=3 and a(2)=0 the second occurrence of 3 is for a(21):
3, 0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, 4, 0, 5, 3, 20, 0, ...
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A171862, A181391, A171911-A171918.

Programs

Maple

P:=proc(q) local a,c,h,i,k,m,n,p,x; m:=60000; a:=Array(1..m); p:=Array(0..m, -1); c:=Array(0..1000);
for k from 0 to 1000 do for i from 0 to m do p[i]:=0; od; for i from 1 to m do a[i]:=0; od;
a[1]:=k; a[2]:=0; p[0]:=2; p[a[1]]:=1; x:=0; for n from 3 to m do h:=p[x]; a[n]:=x; p[x]:=n; x:=0;
if h>0 then x:=n-h; fi; if a[n]=k then c[k]:=x+1; break; fi;
od; od; [seq(c[n], n=0..1000)]; end: P(1);

Formula

a(n) = 1 + A171862(n). - Jan Ritsema van Eck, Jul 24 2019