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%I #22 Apr 03 2022 09:57:47
%S 1,2,4,3,7,5,8,6,9,11,10,14,12,13,16,15,19,17,21,20,22,18,23,25,24,26,
%T 28,27,31,29,32,30,33,35,34,38,36,37,41,39,42,40,43,44,52,45,47,46,50,
%U 48,49,54,55,51,56,53,58,59,57,61,60,62,64,63,67,65,69,68,70,66,71,73,72,74,76,75,79,77,81,80,82,78,83,84,88,85,87,86,89,91,90,94,92
%N a(1)=1; thereafter a(n) = smallest positive integer not among the earlier terms of the sequence such that a(n) and a(n-1) have an even number of common 1-bits in their binary representations
%C A variant of A109812. Sharing an even number of common 1-bits is equivalent to zero correlation between sequences in the vector space F_2^k.
%H Rémy Sigrist, <a href="/A352716/b352716.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A352716/a352716.gp.txt">PARI program</a>
%o (PARI) See Links section.
%o (Python 3.10+)
%o from itertools import islice
%o def A352716_gen(): # generator of terms
%o yield 1
%o l1, s, b = 1, 2, set()
%o while True:
%o i = s
%o while True:
%o if not (i in b or (i & l1).bit_count() % 2):
%o yield i
%o l1 = i
%o b.add(i)
%o while s in b:
%o b.remove(s)
%o s += 1
%o break
%o i += 1
%o A352716_list = list(islice(A352716_gen(),20)) # _Chai Wah Wu_, Apr 02 2022
%Y Cf. A109812, A352715.
%K nonn
%O 1,2
%A _Chai Wah Wu_, _Michael De Vlieger_, _Rémy Sigrist_, and _N. J. A. Sloane_, Mar 30 2022
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