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

%I A216431 #29 Jan 01 2025 15:40:47
%S A216431 0,2,4,7,8,12,15,16,21,24,28,31,32,38,42,46,49,53,56,60,63,64,71,75,
%T A216431 79,82,87,90,94,97,102,106,110,113,117,120,124,127,128,136,143,147,
%U A216431 152,158,162,168,174,178,183,186,190,193,199,203,207,210,215,218,222
%N A216431 a(0)=0; thereafter a(n+1) = a(n) + 1 + number of 0's in binary representation of a(n), counted with A023416.
%C A216431 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.
%H A216431 Harvey P. Dale, <a href="/A216431/b216431.txt">Table of n, a(n) for n = 0..1000</a>
%F A216431 If n<2, a(n) = 2n, otherwise, a(n) = A233272(a(n-1)). - _Antti Karttunen_, Dec 12 2013
%t A216431 NestList[#+1+DigitCount[#,2,0]&,0,60] (* _Harvey P. Dale_, Sep 25 2013 *)
%o A216431 (Python)
%o A216431 a = 0
%o A216431 for n in range(100):
%o A216431     print(a, end=', ')
%o A216431     ta = a
%o A216431     c0 = (a==0)
%o A216431     while ta>0:
%o A216431         c0 += 1-(ta&1)
%o A216431         ta >>= 1
%o A216431     a += 1 + c0
%o A216431 (Scheme)
%o A216431 ;; With memoizing definec-macro from Antti Karttunen's IntSeq-library.
%o A216431 (definec (A216431 n) (if (< n 2) (+ n n) (A233272 (A216431 (- n 1)))))
%o A216431 ;; _Antti Karttunen_, Dec 12 2013
%Y A216431 Differs from A233271 only in that this jumps directly from 0 to 2 in the beginning.
%Y A216431 Cf. A023416, A010062, A214913, A233271, A233272.
%K A216431 nonn,base
%O A216431 0,2
%A A216431 _Alex Ratushnyak_, Sep 08 2012
%E A216431 Name edited by _Antti Karttunen_, Dec 12 2013