

A171898


Forward van Eck transform of A181391.


8



1, 2, 6, 2, 2, 5, 1, 6, 42, 5, 2, 4, 5, 9, 14, 3, 9, 3, 15, 2, 4, 6, 17, 3, 6, 32, 56, 5, 3, 131, 5, 11, 5, 3, 20, 6, 2, 8, 15, 31, 170, 3, 31, 18, 3, 3, 33, 5, 1, 11, 46, 56, 4, 37, 152, 307, 3, 7, 92, 4, 7, 62, 52, 3, 42, 3, 6, 2, 19, 6, 8, 3, 9, 3, 650, 2, 23, 8, 223, 7, 206, 3, 21, 25, 5, 8
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Given a sequence a, the forward van Eck transform b is defined as follows: If a(n) also appears again in a in a later position, let a(m) be the next occurrence, and set b(n)=mn; otherwise b(n)=0.
This is a permutation of the positive terms in A181391, where each term m > 0 from that sequence is shifted backwards m+1 positions.  Jan Ritsema van Eck, Aug 16 2019


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000


FORMULA

From Jan Ritsema van Eck, Aug 16 2019: (Start)
A181391(i+a(i)+1) = a(i) for any i, a(i)>0.
Conversely, a(jA(181391(j)1) = A181391(j) for any j, A181391(j)>0. (End)


MAPLE

ECKf:=proc(a) local b, i, m, n;
if whattype(a) <> list then RETURN([]); fi:
b:=[];
for n from 1 to nops(a)1 do
# does a(n) appear again?
m:=0;
for i from n+1 to nops(a) do
if (a[i]=a[n]) then m:=in; break; fi
od:
b:=[op(b), m];
od:
b:=[op(b), 0];
RETURN(b);
end:


CROSSREFS

Cf. A181391 (van Eck's sequence), A171899, A171942.
Sequence in context: A289382 A062539 A064136 * A330541 A320575 A110218
Adjacent sequences: A171895 A171896 A171897 * A171899 A171900 A171901


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Oct 22 2010


STATUS

approved



