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

Author

Alex Ratushnyak, Sep 08 2012

Keywords

• nonn
• base

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

Crossrefs

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

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

Programs

Mathematica

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

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

Formula

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

Extensions

Name edited by Antti Karttunen, Dec 12 2013