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A359496 Nonnegative integers whose sum of positions of 1's in their binary expansion is less than the sum of positions of 1's in their reversed binary expansion, where positions in a sequence are read starting with 1 from the left.

%I A359496 #12 Mar 07 2023 19:04:19
%S A359496 2,4,6,8,10,12,13,14,16,18,20,22,24,25,26,28,29,30,32,34,36,38,40,41,
%T A359496 42,44,46,48,49,50,52,53,54,56,57,58,59,60,61,62,64,66,68,72,74,76,80,
%U A359496 81,82,84,86,88,89,90,92,94,96,97,98,100,101,102,104,105,106
%N A359496 Nonnegative integers whose sum of positions of 1's in their binary expansion is less than the sum of positions of 1's in their reversed binary expansion, where positions in a sequence are read starting with 1 from the left.
%C A359496 First differs from A161602 in lacking 70, with binary expansion (1,0,0,0,1,1,0), positions of 1's 1 + 5 + 6 = 12, reversed 2 + 3 + 7 = 12.
%F A359496 A230877(a(n)) < A029931(a(n)).
%e A359496 The initial terms, binary expansions, and positions of 1's are:
%e A359496     2:      10 ~ {2}
%e A359496     4:     100 ~ {3}
%e A359496     6:     110 ~ {2,3}
%e A359496     8:    1000 ~ {4}
%e A359496    10:    1010 ~ {2,4}
%e A359496    12:    1100 ~ {3,4}
%e A359496    13:    1101 ~ {1,3,4}
%e A359496    14:    1110 ~ {2,3,4}
%e A359496    16:   10000 ~ {5}
%e A359496    18:   10010 ~ {2,5}
%e A359496    20:   10100 ~ {3,5}
%e A359496    22:   10110 ~ {2,3,5}
%e A359496    24:   11000 ~ {4,5}
%e A359496    25:   11001 ~ {1,4,5}
%e A359496    26:   11010 ~ {2,4,5}
%e A359496    28:   11100 ~ {3,4,5}
%e A359496    29:   11101 ~ {1,3,4,5}
%e A359496    30:   11110 ~ {2,3,4,5}
%t A359496 Select[Range[100],Total[Accumulate[IntegerDigits[#,2]]]>Total[Accumulate[Reverse[IntegerDigits[#,2]]]]&]
%o A359496 (Python 3.10+)
%o A359496 from itertools import count, islice
%o A359496 def A359496_gen(startvalue=0): # generator of terms >= startvalue
%o A359496     return filter(lambda n:sum(i for i, j in enumerate(bin(n)[2:]) if j=='1')<<1 < n.bit_count()*(n.bit_length()-1), count(max(startvalue,0)))
%o A359496 A359496_list = list(islice(A359496_gen(),20)) # _Chai Wah Wu_, Jan 19 2023
%Y A359496 The opposite version is A359401.
%Y A359496 Indices of negative terms in A359495; indices of 0's are A359402.
%Y A359496 A030190 gives binary expansion, reverse A030308.
%Y A359496 A070939 counts binary digits.
%Y A359496 A230877 adds up positions of 1's in binary expansion, reverse A029931.
%Y A359496 A326669 lists numbers with integer mean position of a 1 in binary expansion.
%Y A359496 A358194 counts partitions by sum of partial sums, compositions A053632.
%Y A359496 Cf. A000120, A048793, A051293, A222955, A231204, A291166, A304818, A326672, A326673, A359043.
%K A359496 nonn,base
%O A359496 1,1
%A A359496 _Gus Wiseman_, Jan 18 2023