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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A322590 A325381 A323898 * A324531 A323897 A324530

Adjacent sequences:  A323231 A323232 A323233 * A323235 A323236 A323237

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Jan 08 2019

STATUS

approved

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Last modified December 15 11:43 EST 2019. Contains 329999 sequences. (Running on oeis4.)