A181988 If n is odd, a(n) = (n+1)/2; if n is even, a(n) = a(n/2) + A003602(n).

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, 16, 16, 6, 17, 18, 18, 15, 19, 20, 20, 12, 21, 22, 22, 18, 23, 24, 24, 10, 25, 26, 26, 21, 27, 28, 28, 16, 29, 30, 30, 24, 31, 32, 32, 7, 33, 34, 34, 27, 35, 36

Offset: 1

Author

David Spies, Apr 04 2012

Keywords

• easy
• nonn

Comments

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

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

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191

Crossrefs

Cf. A220466.

Cf. A001511, A003602.

Programs

Haskell

interleave (hdx : tlx) y = hdx : interleave y tlx
oeis003602 = interleave [1..] oeis003602
oeis181988 = interleave [1..] (zipWith (+) oeis003602 oeis181988)

Maple

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

Python

from itertools import count
def interleave(A):
    A1=next(A)
    A2=interleave(A)
    while True:
        yield next(A1)
        yield next(A2)
def multiples(k):
    return (k*i for i in count(1))
interleave(multiples(k) for k in count(1))

Python

def A181988(n): return (m:=(n&-n).bit_length())*((n>>m)+1) # Chai Wah Wu, Jul 12 2022

Scheme

;; With memoization-macro definec.
(definec (A181988 n) (if (even? n) (+ (A003602 n) (A181988 (/ n 2))) (A003602 n)))
;; Antti Karttunen, Jan 19 2016

Formula

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

a(n) = A001511(n)*A003602(n). - L. Edson Jeffery, Nov 21 2015. (Follows directly from above formula.) - Antti Karttunen, Jan 19 2016

Extensions

Definition replaced by a formula provided by David Spies, Sep 17 2012. N. J. A. Sloane, Nov 22 2015