A171934 Backwards van Eck transform of A000010.

0, 1, 0, 1, 0, 2, 0, 3, 2, 2, 0, 2, 0, 5, 0, 1, 0, 4, 0, 4, 8, 11, 0, 4, 0, 5, 8, 2, 0, 6, 0, 15, 8, 2, 0, 8, 0, 11, 4, 6, 0, 6, 0, 11, 6, 23, 0, 8, 6, 6, 0, 7, 0, 16, 14, 4, 20, 29, 0, 12, 0, 31, 6, 13, 0, 16, 0, 4, 0, 14, 0, 2, 0, 11, 20, 2, 16, 6, 0, 12, 0, 7, 0, 6, 0, 37, 0, 6, 0, 6, 18, 23, 16, 47

Offset

1,6

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. (Comment from A171899).

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

N. J. A. Sloane, Transforms

Mathematica

Block[{a = Array[EulerPhi, 94], b = {}, m}, Do[If[! IntegerQ[m[#]], Set[m[#], i]; AppendTo[b, 0], AppendTo[b, i - m[#]]; Set[m[#], i]] &@ a[[i]], {i, Length[a]}]; b] (* Michael De Vlieger, Apr 06 2021 *)

Prog

(PARI)
up_to = 105;
backVanEck_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = i-pp, outvec[i] = 0); mapput(om, invec[i], i)); outvec; };
v171934 = backVanEck_transform(vector(up_to, n, eulerphi(n)));
A171934(n) = v171934[n]; \\ Antti Karttunen, Apr 06 2021

Crossrefs

Cf. A000010.

Cf. also A081373, A171899, A171900, A171932, A171933, A171936, A171941.

Sequence in context: A242029 A090722 A221879 * A303205 A082785 A100949

Adjacent sequences: A171931 A171932 A171933 * A171935 A171936 A171937

Keyword

nonn

Author

N. J. A. Sloane, Oct 24 2010

Status

approved