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Positive integers k such that A000120(k) > A001511(k).
5

%I #29 Jun 09 2024 02:41:57

%S 3,5,7,9,11,13,14,15,17,19,21,22,23,25,26,27,29,30,31,33,35,37,38,39,

%T 41,42,43,45,46,47,49,50,51,53,54,55,57,58,59,60,61,62,63,65,67,69,70,

%U 71,73,74,75,77,78,79,81,82,83,85,86,87,89,90,91,92,93,94,95,97,98,99

%N Positive integers k such that A000120(k) > A001511(k).

%C Numbers whose binary expansion does not encode for any Schreier set (cf. A371176 and A373345).

%C All odd numbers > 1 are terms.

%H Paolo Xausa, <a href="/A373347/b373347.txt">Table of n, a(n) for n = 1..10000</a>

%F a(k) = 2^(n+1) - 1; a(k+1) = 2^(n+1) + 1, where k = A008466(n+1).

%t Select[Range[100], DigitCount[#, 2, 1] > IntegerExponent[#, 2] + 1 &]

%o (Python)

%o def isa(n): return (n - 1).bit_count() < ((n.bit_count() - 1) << 1)

%o print([n for n in range(100) if isa(n)]) # _Peter Luschny_, Jun 07 2024

%o (PARI) isok(k) = hammingweight(k) > valuation(2*k, 2); \\ _Michel Marcus_, Jun 07 2024

%Y Complement of A371176.

%Y Cf. A000120, A001511, A008466, A373345, A373360 (first differences).

%K nonn,easy,base

%O 1,1

%A _Paolo Xausa_, Jun 01 2024