A323234 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 0, and for n > 1, f(n) = ordered pair [A053645(n), A079944(n-2)], where A053645(n) gives n without its most significant bit, while A079944(n-2) gives the second most significant bit of n.

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

Offset

1,2

Comments

Also the restricted growth sequence transform of function f(1) = 0, f(n) = [A053645(n), A278222(n)] for n > 1.

For all i, j:

a(i) = a(j) => A286622(i) = A286622(j),

a(i) = a(j) => A323235(i) = A323235(j),

a(i) = a(j) => A323236(i) = A323236(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to binary expansion of n

Prog

(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; };
A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644
A053645(n) = (n-A053644(n));
A079944off0(n) = (1==binary(2+n)[2]);
A323234aux(n) = if(1==n, 0, [A053645(n), A079944off0(n-2)]);
v323234 = rgs_transform(vector(up_to, n, A323234aux(n)));
A323234(n) = v323234[n];

Crossrefs

Cf. A053645, A079944, A278222, A286622, A323235, A323236.

Cf. also A300226 (an analogous filter sequence for prime factorization).

Sequence in context: A336152 A323898 A336154 * A336156 A336474 A336148

Adjacent sequences: A323231 A323232 A323233 * A323235 A323236 A323237

Keyword

nonn,base

Author

Antti Karttunen, Jan 08 2019

Status

approved