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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
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
1,2
COMMENTS
We call a(n) the multiplicative index of odious-evil stability of 2*n-1.
LINKS
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.
EXAMPLE
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.
PROG
(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
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Oct 21 2013
EXTENSIONS
a(17)-a(87) from Charles R Greathouse IV, Oct 22 2013
STATUS
approved