A331173 -id:A331173 - cp's OEIS frontend

A331166 a(n) = min(n, A057889(n)), where A057889 is bijective base-2 reverse.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 19, 22, 27, 28, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 37, 42, 43, 44, 45, 46, 47, 48, 35, 38, 51, 44, 43, 54, 55, 56, 39, 46, 55, 60, 47, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 69, 74, 83, 84, 85, 86, 87, 88, 77, 90, 91, 92, 93, 94, 95, 96, 67, 70

Offset: 0

Antti Karttunen, Jan 12 2020

There is a large number of sequences b, related to binary expansion of n (A007088), for which it holds that b(n) = b(a(n)) for all n >= 0 (or n >= 1). For example, we have:
For all i, j:
  a(i) = a(j) => A002487(i) = A002487(j),
  a(i) = a(j) => A005811(i) = A005811(j),
  a(i) = a(j) => A286622(i) = A286622(j) => A000120(i) = A000120(j).
For all i, j > 0:
  a(i) = a(j) => A007814(i) = A007814(j),
  a(i) = a(j) => A280505(i) = A280505(j),
  a(i) = a(j) => A305788(i) = A305788(j) => A091222(i) = A091222(j).

Antti Karttunen, Table of n, a(n) for n = 0..16383
Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A000120, A002487, A005811, A007088, A007814, A030101, A057889, A091222, A280505, A286622, A305788.

Cf. also A330740, A331167, A331173.

A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
A331166(n) = min(n, A057889(n));

a(n) = min(n, A057889(n)).

A331303 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = min(n, A263273(n)), and A263273 is bijective base-3 reverse.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 11, 19, 15, 14, 20, 21, 17, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 27, 33, 34, 35, 36, 37, 38, 39, 40, 30, 41, 42, 38, 43, 44, 45, 46, 47, 25, 48, 29, 33, 49, 50, 41, 51, 40, 28, 49, 37, 36, 52, 53, 43, 54, 55, 31, 51, 44, 39, 54, 56, 46, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69

Offset: 0

Antti Karttunen, Jan 18 2020

Restricted growth sequence transform of A331173. See comments in that sequence.

Antti Karttunen, Table of n, a(n) for n = 0..100000

Cf. A263273, A331173.

Cf. also A331300.

up_to = 100000;
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; };
A030102(n) = { my(r=[n%3]); while(0A263273 = n -> if(!n,n,A030102(n/(3^valuation(n,3))) * (3^valuation(n, 3)));
A331173(n) = min(n, A263273(n));
v331303 = rgs_transform(vector(1+up_to,n,A331173(n-1)));
A331303(n) = v331303[1+n];

cp's OEIS Frontend

A331166 a(n) = min(n, A057889(n)), where A057889 is bijective base-2 reverse.

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