A233419 -id:A233419 - cp's OEIS frontend

1, 2, 7, 13, 14, 21, 25, 26, 31, 37, 41, 42, 49, 50, 55, 61, 62, 69, 73, 74, 81, 82, 87, 93, 97, 98, 103, 109, 110, 117, 121, 122, 127, 133, 137, 138, 145, 146, 151, 157, 161, 162, 167, 173, 174, 181, 185, 186, 193, 194, 199, 205, 206, 213, 217, 218, 223, 229, 233, 234, 241, 242, 247, 253

Offset: 1

Gerasimov Sergey, Nov 27 2013

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

			The first odious number, A000069(1) = 1, and A000069(1) = 1, so a(1) = 1.
The second odious number, A000069(2) = 2, and A000069(2) = 2, so a(2) = 2.
Those were the only fixed points of A000069, and after that, we have:
The third odious number, A000069(3) = 4, and A000069(4) = 7, thus a(3) = 7.
The fourth odious number, A000069(4) = 7, and A000069(7) = 13, thus a(4) = 13.

Antti Karttunen, Table of n, a(n) for n = 1..8193

Cf. A000069, A102615, A092246, A232667, A233419.
A004119 from term 7 onward is a subsequence.
Subsequence of A042968.

a(n)=4*n-if(hammingweight(n-1)%2,if(hammingweight(n-2)%2,5,6),3) \\ Charles R Greathouse IV, Dec 05 2013

(define (A232637 n) (A000069 (A000069 n)))

a(n) = A000069(A000069(n)).

4n-6 <= a(n) <= 4n-3, see PARI script. - Charles R Greathouse IV, Dec 05 2013

cp's OEIS Frontend

A232637 Odious numbers of order 2: a(n) = A000069(A000069(n)).

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