A216431 a(0)=0; thereafter a(n+1) = a(n) + 1 + number of 0's in binary representation of a(n), counted with A023416.

0, 2, 4, 7, 8, 12, 15, 16, 21, 24, 28, 31, 32, 38, 42, 46, 49, 53, 56, 60, 63, 64, 71, 75, 79, 82, 87, 90, 94, 97, 102, 106, 110, 113, 117, 120, 124, 127, 128, 136, 143, 147, 152, 158, 162, 168, 174, 178, 183, 186, 190, 193, 199, 203, 207, 210, 215, 218, 222

Offset

0,2

Comments

The difference from A233271 stems from the fact that it uses A080791 to count the 0-bits in binary expansion of n, while this sequence uses A023416, which results a slightly different start for the iteration.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

If n<2, a(n) = 2n, otherwise, a(n) = A233272(a(n-1)). - Antti Karttunen, Dec 12 2013

Mathematica

NestList[#+1+DigitCount[#, 2, 0]&, 0, 60] (* Harvey P. Dale, Sep 25 2013 *)

Prog

(Python)
a = 0
for n in range(100):
    print(a, end=', ')
    ta = a
    c0 = (a==0)
    while ta>0:
        c0 += 1-(ta&1)
        ta >>= 1
    a += 1 + c0
(Scheme)
;; With memoizing definec-macro from Antti Karttunen's IntSeq-library.
(definec (A216431 n) (if (< n 2) (+ n n) (A233272 (A216431 (- n 1)))))
;; Antti Karttunen, Dec 12 2013

Crossrefs

Differs from A233271 only in that this jumps directly from 0 to 2 in the beginning.

Cf. A023416, A010062, A214913, A233271, A233272.

Sequence in context: A001839 A087686 A232054 * A233271 A088413 A372098

Adjacent sequences: A216428 A216429 A216430 * A216432 A216433 A216434

Keyword

nonn,base

Author

Alex Ratushnyak, Sep 08 2012

Extensions

Name edited by Antti Karttunen, Dec 12 2013

Status

approved