A344180 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 0, where f(n) = 0 if n is a Fibbinary number (A003714), otherwise f(n) = n.

1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 1, 5, 6, 7, 8, 9, 1, 1, 1, 10, 1, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 1, 1, 21, 1, 1, 22, 23, 1, 1, 1, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 1, 1, 1, 45, 1, 1, 46, 47, 1, 1, 1, 48, 49, 50, 51, 52, 1, 1, 1, 53, 1, 1, 54, 55, 56, 57

Offset: 0

Author

Antti Karttunen, May 16 2021

Keywords

• nonn

Comments

For all i, j:

a(i) = a(j) => A085357(i) = A085357(j),

a(i) = a(j) => A213370(i) = A213370(j),

a(i) = a(j) => A344182(i) = A344182(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A003714 (positions of 1's), A085357, A213370, A344182.

Cf. also A324400.

Programs

PARI

up_to = 65537;
rgs_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] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
Aux344180(n) = if(!bitand(n,n+n),0,n);
v344180 = rgs_transform(vector(1+up_to,n,Aux344180(n-1)));
A344180(n) = v344180[1+n];