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A342378 List of numbers whose binary expansion is an instance of the Zimin pattern ABA.

%I A342378 #20 Mar 10 2021 01:38:58
%S A342378 5,7,9,11,13,15,17,18,19,21,22,23,25,27,29,31,33,34,35,37,38,39,41,42,
%T A342378 43,45,46,47,49,51,53,55,57,59,61,63,65,66,67,68,69,70,71,73,74,75,76,
%U A342378 77,78,79,81,82,83,85,86,87,89,90,91,93,94,95,97,99,101
%N A342378 List of numbers whose binary expansion is an instance of the Zimin pattern ABA.
%C A342378 This is A091066 with some terms of A020330 removed.
%H A342378 Peter Kagey, <a href="/A342378/b342378.txt">Table of n, a(n) for n = 1..1000</a>
%H A342378 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sesquipower">Sesquipower</a>
%e A342378 The binary expansion of 182 is 10110110, which is an instance of the pattern ABA with A=10 and B=1101.
%o A342378 (Python)
%o A342378 def ok(n):
%o A342378   b = bin(n)[2:]
%o A342378   for i in range(1, (len(b)+1)//2):
%o A342378     if b[:i] == b[-i:]: return True
%o A342378   return False
%o A342378 def aupto(lim): return [m for m in range(lim+1) if ok(m)]
%o A342378 print(aupto(101)) # _Michael S. Branicky_, Mar 09 2021
%Y A342378 Cf. A020330, A091066, A254128, A262312.
%K A342378 nonn,base
%O A342378 1,1
%A A342378 _Peter Kagey_, Mar 09 2021