%I #45 Jul 12 2022 09:50:04

%S 1,2,2,3,3,4,4,4,5,6,6,6,7,8,8,5,9,10,10,9,11,12,12,8,13,14,14,12,15,

%T 16,16,6,17,18,18,15,19,20,20,12,21,22,22,18,23,24,24,10,25,26,26,21,

%U 27,28,28,16,29,30,30,24,31,32,32,7,33,34,34,27,35,36

%N If n is odd, a(n) = (n+1)/2; if n is even, a(n) = a(n/2) + A003602(n).

%C The original definition was "Interleaved multiples of the positive integers".

%C This sequence is A_1 where A_k = Interleave(k*counting,A_(k+1)).

%C Show your friends the first 15 terms and see if they can guess term number 16. (If you want to be fair, you might want to show them A003602 first.) - _David Spies_, Sep 17 2012

%H Antti Karttunen, <a href="/A181988/b181988.txt">Table of n, a(n) for n = 1..8191</a>

%F a((2*n-1)*2^p) = n*(p+1), p >= 0.

%F a(n) = A001511(n)*A003602(n). - _L. Edson Jeffery_, Nov 21 2015. (Follows directly from above formula.) - _Antti Karttunen_, Jan 19 2016

%p nmax:=70: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 1 to ceil(nmax/(p+2)) do a((2*n-1)*2^p) := n*(p+1) od: od: seq(a(n), n=1..nmax); # _Johannes W. Meijer_, Jan 21 2013

%o (Haskell)

%o interleave (hdx : tlx) y = hdx : interleave y tlx

%o oeis003602 = interleave [1..] oeis003602

%o oeis181988 = interleave [1..] (zipWith (+) oeis003602 oeis181988)

%o (Python)

%o from itertools import count

%o def interleave(A):

%o A1=next(A)

%o A2=interleave(A)

%o while True:

%o yield next(A1)

%o yield next(A2)

%o def multiples(k):

%o return (k*i for i in count(1))

%o interleave(multiples(k) for k in count(1))

%o (Python)

%o def A181988(n): return (m:=(n&-n).bit_length())*((n>>m)+1) # _Chai Wah Wu_, Jul 12 2022

%o (Scheme, with memoization-macro definec)

%o (definec (A181988 n) (if (even? n) (+ (A003602 n) (A181988 (/ n 2))) (A003602 n)))

%o ;; _Antti Karttunen_, Jan 19 2016

%Y Cf. A220466.

%Y Cf. A001511, A003602.

%K easy,nonn

%O 1,2

%A _David Spies_, Apr 04 2012

%E Definition replaced by a formula provided by _David Spies_, Sep 17 2012. _N. J. A. Sloane_, Nov 22 2015