A361479 a(n) is the least integer whose binary expansion has the same multiset of run-lengths as that of n.

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

Offset: 0

Author

Rémy Sigrist, Mar 13 2023

Keywords

• nonn
• base

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A073137, A361478, A361480.

Programs

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); }

Formula

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

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