A361478 -id:A361478

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Search: a361478 -id:a361478

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A361481

Distinct values of A361478, in order of appearance.

+20
2

0, 1, 2, 3, 4, 6, 5, 7, 8, 14, 9, 11, 13, 10, 12, 15, 16, 30, 17, 23, 29, 18, 20, 22, 26, 19, 25, 27, 21, 24, 28, 31, 32, 62, 33, 47, 61, 34, 40, 46, 58, 35, 39, 49, 55, 57, 59, 36, 38, 44, 50, 52, 54, 37, 41, 43, 45, 53, 42, 48, 60, 51, 56, 63, 64, 126, 65

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

This sequence is a permutation of the nonnegative integers with inverse A361482.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) < 2^k iff n < 2^k.

PROG

(PARI) See Links section.

CROSSREFS

Cf. A361478, A361482 (inverse).

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Mar 14 2023

STATUS

approved

A361479

a(n) is the least integer whose binary expansion has the same multiset of run-lengths as that of n.

+10
3

0, 1, 2, 3, 4, 5, 4, 7, 8, 9, 10, 9, 12, 9, 8, 15, 16, 17, 18, 19, 18, 21, 18, 17, 24, 19, 18, 19, 24, 17, 16, 31, 32, 33, 34, 35, 36, 37, 36, 35, 34, 37, 42, 37, 36, 37, 34, 33, 48, 35, 36, 51, 36, 37, 36, 35, 56, 35, 34, 35, 48, 33, 32, 63, 64, 65, 66, 67

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

FORMULA

a(a(n)) = a(n).

a(n) <= n with equality iff n = 0 or belongs to A175020.

PROG

(PARI) a(n) = { my (r=[]); while (n, my (v=valuation(n+n%2, 2)); n\=2^v; r=concat(v, r)); r=vecsort(r); my (h=0, t=#r+1, v=0); for (k=1, #r, v=(v+k%2)*2^if (k%2, r[h++], r[t--])-k%2; ); return (v); }

CROSSREFS

Cf. A073137, A361478, A361480.

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Mar 13 2023

STATUS

approved

A361480

a(n) is the greatest integer whose binary expansion has the same multiset of run-lengths as that of n.

+10
3

0, 1, 2, 3, 6, 5, 6, 7, 14, 13, 10, 13, 12, 13, 14, 15, 30, 29, 26, 27, 26, 21, 26, 29, 28, 27, 26, 27, 28, 29, 30, 31, 62, 61, 58, 59, 54, 53, 54, 59, 58, 53, 42, 53, 54, 53, 58, 61, 60, 59, 54, 51, 54, 53, 54, 59, 56, 59, 58, 59, 60, 61, 62, 63, 126, 125

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Index entries for sequences related to binary expansion of n

FORMULA

a(a(n)) = a(n).

a(n) >= n.

PROG

(PARI) a(n) = { my (r=[]); while (n, my (v=valuation(n+n%2, 2)); n\=2^v; r=concat(v, r)); r=vecsort(r); my (h=0, t=#r+1, v=0); for (k=1, #r, v=(v+k%2)*2^if (k%2, r[t--], r[h++])-k%2; ); return (v); }

CROSSREFS

Cf. A073138, A335835, A361478, A361479.

KEYWORD

nonn,look,base

AUTHOR

Rémy Sigrist, Mar 13 2023

STATUS

approved

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