A230500 Indices of "power odious-evil stability" of odd integers 2*n-1 > 1 (see comment).

3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 3, 4, 1, 2, 1, 3, 1, 1, 2, 1, 2, 1, 3, 1, 3, 2, 4, 4, 1, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 2, 1, 2, 1, 1, 3, 2, 1, 8, 4, 1, 1, 2, 1, 1, 3, 2, 2, 2, 1, 2, 1, 3, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 1, 3, 3, 1, 1, 2, 3, 1, 1, 3, 1

Offset: 2

Author

Vladimir Shevelev, Oct 21 2013

Keywords

• nonn
• base

Comments

We say that odious 2*n-1, n>=2, has "power odious-evil stability" of index k, if k is the maximal, such that the numbers 2*n-1, (2n-1)^2, ... , (2n-1)^k all are evil or all are odious.

For example, 3, 3^2, 3^3 are evil, while 3^4 is odious. So 3 has power stability of index 3. For 5 it is 1, for 7 it is 2, etc.

Links

• Peter J. C. Moses, Table of n, a(n) for n = 2..10001
• Vladimir Shevelev, "Odious-evil stability" of integers

Crossrefs

Cf. A000069, A001969, A230454, A230495, A230496, A230497, A230498.