A230499 a(n) is the maximal number k of consecutive numbers of the form (2*n-1)*(2*i-1), i=1,2,...,k, which are all evil or all odious (A000069, A001969).

1, 3, 2, 4, 4, 1, 1, 9, 8, 1, 1, 1, 1, 1, 1, 16, 16, 1, 1, 1, 1, 3, 4, 1, 1, 3, 2, 1, 1, 1, 1, 33, 32, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 5, 1, 1, 5, 2, 4, 20, 4, 3, 1, 1, 4, 2, 1, 1, 1, 1, 64, 64, 1, 1, 1, 1, 2, 4, 1, 1, 3, 4, 5, 4, 3, 2, 1, 1, 2, 4, 3, 3, 1, 1

Offset: 1

Author

Vladimir Shevelev, Oct 21 2013

Keywords

• nonn
• base

Comments

We call a(n) the multiplicative index of odious-evil stability of 2*n-1.

Examples

			For n=2, t=2*n-1=3. We see that 3*1=3, 3*3=9,3*5=15 are evil, but 3*7=21 is odious. So, a(2)=3.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• V. Shevelev, "Odious-evil stability" of integers

Crossrefs

Cf. A000069, A001969, A230454, A230495, A230496, A230497, A230498, A000225, A224072.

Programs

PARI

a(n)=my(t=2*n-1,H=hammingweight(t)%2,i=3); while(H == hammingweight(i*t)%2, i+=2); i\2 \\ Charles R Greathouse IV, Oct 22 2013

Formula

If 2*n-1 is Mersenne number (A000225), then a(n)>=n; if 2*n-1 is odious such that 6*n-3 is not in A224072, then a(n)=1.

Extensions

a(17)-a(87) from Charles R Greathouse IV, Oct 22 2013