A171899 Backwards van Eck transform of A000002.

0, 0, 1, 3, 1, 3, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 1, 3, 2, 1, 3, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 1, 3, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2, 1, 3, 1, 3, 2, 1, 3, 1, 3, 2, 2, 1, 3

Offset: 1

Author

N. J. A. Sloane, Oct 22 2010

Keywords

• nonn

Comments

Given a sequence a, the backwards van Eck transform b is defined as follows: If a(n) has already appeared in a, let a(m) be the most recent occurrence, and set b(n)=n-m; otherwise b(n)=0.

The forwards van Eck transform of A000002 is A078929.

Crossrefs

Cf. A000002, A181391, A171898, A078929.

Programs

Maple

ECKb:=proc(a) local b,i,m,n;
if whattype(a) <> list then RETURN([]); fi:
b:=[0];
for n from 2 to nops(a) do
# has a(n) appeared before?
m:=0;
for i from n-1 by -1 to 1 do
if (a[i]=a[n]) then m:=n-i; break; fi
od:
b:=[op(b),m];
od:
RETURN(b);
end: