A341231 -id:A341231 - cp's OEIS frontend

A341235 a(n) is the greatest term in n-th row of A341231.

1, 2, 4, 4, 14, 6, 8, 8, 28, 14, 28, 12, 28, 14, 16, 16, 62, 28, 52, 20, 62, 28, 56, 24, 62, 28, 44, 28, 52, 30, 32, 32, 122, 62, 100, 36, 110, 52, 104, 40, 122, 62, 124, 44, 118, 56, 112, 48, 122, 62, 84, 52, 112, 54, 88, 56, 110, 58, 76, 60, 100, 62, 64, 64

Offset: 1

Rémy Sigrist, Feb 07 2021

Records of a(n)/n appear to happen for n in A083318.

			For n = 10:
- the trajectory of 10 under A245471 is 10 -> 5 -> 14 -> 7 -> 8 -> 4 -> 2 -> 1,
- so a(10) = 14.

Cf. A025586, A083318, A245471, A340873, A341231.

a(n) = { my (m=n); while (n>1, m=max(m, n=if (n%2, bitxor(n, 2*n+1), n/2))); m }

a(n) >= n, equality implies that n equals 1 or is even.

a(n) < 4*n.

A340873 a(n) is the number of iterations of A245471 needed to reach 1 starting from n.

Original entry on oeis.org

0, 1, 3, 2, 6, 4, 4, 3, 11, 7, 7, 5, 9, 5, 5, 4, 12, 12, 12, 8, 8, 8, 8, 6, 10, 10, 10, 6, 14, 6, 6, 5, 21, 13, 13, 13, 13, 13, 13, 9, 17, 9, 9, 9, 17, 9, 9, 7, 19, 11, 11, 11, 11, 11, 11, 7, 15, 15, 15, 7, 15, 7, 7, 6, 22, 22, 22, 14, 14, 14, 14, 14, 22, 14

Offset: 1

Rémy Sigrist, Jan 31 2021

This sequence is well defined.
Sketch of proof:
- we focus on odd numbers n > 1,
- if the binary representation of n ends with k 0's and one 1:
       in two steps we obtain a number with the same binary length as n
       and ending with k-1 0's and one 1,
       iterating again will eventually give a number ending with two or more 1's,
- if the binary representation of n ends with k 1's (k > 1):
       in k+1 steps we obtain a number with a binary length strictly smaller
       than that of n,
- so any odd number > 1 will eventually reach the number 1.

			For n = 10:
- the trajectory of 10 is 10 -> 5 -> 14 -> 7 -> 8 -> 4 -> 2 -> 1,
- so a(10) = 7.

Cf. A006577, A245471, A341194, A341218, A341220, A341231, A341235.

a(n) = for (k=0, oo, if (n==1, return (k), n%2, n=bitxor(n, 2*n+1), n=n/2))

a(2*n) = a(n) + 1.

cp's OEIS Frontend

A341235 a(n) is the greatest term in n-th row of A341231.

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