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.

2, 4, 6, 8, 10, 12, 13, 14, 16, 18, 20, 22, 24, 25, 26, 28, 29, 30, 32, 34, 36, 38, 40, 41, 42, 44, 46, 48, 49, 50, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 64, 66, 68, 72, 74, 76, 80, 81, 82, 84, 86, 88, 89, 90, 92, 94, 96, 97, 98, 100, 101, 102, 104, 105, 106

Offset: 1

Author

Gus Wiseman, Jan 18 2023

Keywords

• nonn
• base

Comments

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.

Examples

			The initial terms, binary expansions, and positions of 1's are:
    2:      10 ~ {2}
    4:     100 ~ {3}
    6:     110 ~ {2,3}
    8:    1000 ~ {4}
   10:    1010 ~ {2,4}
   12:    1100 ~ {3,4}
   13:    1101 ~ {1,3,4}
   14:    1110 ~ {2,3,4}
   16:   10000 ~ {5}
   18:   10010 ~ {2,5}
   20:   10100 ~ {3,5}
   22:   10110 ~ {2,3,5}
   24:   11000 ~ {4,5}
   25:   11001 ~ {1,4,5}
   26:   11010 ~ {2,4,5}
   28:   11100 ~ {3,4,5}
   29:   11101 ~ {1,3,4,5}
   30:   11110 ~ {2,3,4,5}
		

Crossrefs

The opposite version is A359401.

Indices of negative terms in A359495; indices of 0's are A359402.

A030190 gives binary expansion, reverse A030308.

A070939 counts binary digits.

A230877 adds up positions of 1's in binary expansion, reverse A029931.

A326669 lists numbers with integer mean position of a 1 in binary expansion.

A358194 counts partitions by sum of partial sums, compositions A053632.

Cf. A000120, A048793, A051293, A222955, A231204, A291166, A304818, A326672, A326673, A359043.

Programs

Mathematica

Select[Range[100],Total[Accumulate[IntegerDigits[#,2]]]>Total[Accumulate[Reverse[IntegerDigits[#,2]]]]&]

Formula

A230877(a(n)) < A029931(a(n)).