OFFSET
1,2
COMMENTS
Odious numbers with odious subscripts.
From Antti Karttunen, Nov 29 2013: (Start)
Starting from 4 and iterating A000069(4), A000069(A000069(4)), A000069(A000069(A000069(4))), etc. gives A004119 from its second term onward: 4, 7, 13, 25, 49, 97, 193, ..., which is thus a subsequence of this sequence from the term 7 onward.
Proof: All of the terms A004119(n) are odious although A004119(n)-1 is evil, and the formula for A000069(n) reduces to a(n) = 2n - 1 when n-1 is evil, and iterating that formula starting from 4 gives A004119 from 7 onward (cf. Philippe Deléham's formula there dated Feb 20 2004).
(End)
These numbers are never multiples of 4. Probably there are infinitely many multiples of m in this sequence for any m not divisible by 4. Equivalently, A233419(n) > 0 for all n. - Charles R Greathouse IV, Dec 05 2013
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..8193
FORMULA
4n-6 <= a(n) <= 4n-3, see PARI script. - Charles R Greathouse IV, Dec 05 2013
EXAMPLE
Those were the only fixed points of A000069, and after that, we have:
PROG
(Scheme)
(PARI) a(n)=4*n-if(hammingweight(n-1)%2, if(hammingweight(n-2)%2, 5, 6), 3) \\ Charles R Greathouse IV, Dec 05 2013
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Gerasimov Sergey, Nov 27 2013
STATUS
approved