A361480 -id:A361480 - cp's OEIS frontend

A361478 Irregular table T(n, k), n >= 0, k = 1..A361477(n), read by rows; the n-th row lists the integers whose binary expansions have the same multiset of run-lengths as that of n.

0, 1, 2, 3, 4, 6, 5, 4, 6, 7, 8, 14, 9, 11, 13, 10, 9, 11, 13, 12, 9, 11, 13, 8, 14, 15, 16, 30, 17, 23, 29, 18, 20, 22, 26, 19, 25, 27, 18, 20, 22, 26, 21, 18, 20, 22, 26, 17, 23, 29, 24, 28, 19, 25, 27, 18, 20, 22, 26, 19, 25, 27, 24, 28, 17, 23, 29, 16, 30

Offset: 0

Rémy Sigrist, Mar 13 2023

This sequence has similarities with A187786; here we consider multisets of run-lengths, there multisets of digits in binary expansions.

			Table T(n, k) begins (in decimal and in binary):
  n   n-th row    bin(n)  n-th row in binary
  --  ----------  ------  ------------------
   0  0                0  0
   1  1                1  1
   2  2               10  10
   3  3               11  11
   4  4, 6           100  100, 110
   5  5              101  101
   6  4, 6           110  100, 110
   7  7              111  111
   8  8, 14         1000  1000, 1110
   9  9, 11, 13     1001  1001, 1011, 1101
  10  10            1010  1010
  11  9, 11, 13     1011  1001, 1011, 1101
  12  12            1100  1100
  13  9, 11, 13     1101  1001, 1011, 1101
  14  8, 14         1110  1000, 1110
  15  15            1111  1111
  16  16, 30       10000  10000, 11110

Rémy Sigrist, Table of n, a(n) for n = 0..6009 (rows for n = 0..511 flattened)
Rémy Sigrist, PARI program
Index entries for sequences related to binary expansion of n

Cf. A187786, A361477, A361479, A361480.

PARI
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See Links section.
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T(n, 1) = A361479(n).

T(n, A361477(n)) = A361480(n).

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

Original entry on oeis.org

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

Rémy Sigrist, Mar 13 2023

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

Cf. A073137, A361478, A361480.

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); }

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

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

cp's OEIS Frontend

A361478 Irregular table T(n, k), n >= 0, k = 1..A361477(n), read by rows; the n-th row lists the integers whose binary expansions have the same multiset of run-lengths as that of n.

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