A359401 Nonnegative integers whose sum of positions of 1's in their binary expansion is greater 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.

11, 19, 23, 35, 37, 39, 43, 47, 55, 67, 69, 71, 75, 77, 79, 83, 87, 91, 95, 103, 111, 131, 133, 134, 135, 137, 139, 141, 142, 143, 147, 149, 151, 155, 157, 158, 159, 163, 167, 171, 173, 175, 179, 183, 187, 191, 199, 203, 207, 215, 223, 239, 259, 261, 262, 263

Offset

1,1

Comments

First differs from A161601 in having 134, with binary expansion (1,0,0,0,0,1,1,0), positions of 1's 1 + 6 + 7 = 14, reversed 2 + 3 + 8 = 13.

Links

Table of n, a(n) for n=1..56.

Formula

A230877(a(n)) > A029931(a(n)).

Mathematica

sap[q_]:=Sum[q[[i]]*(2i-Length[q]-1), {i, Length[q]}];
Select[Range[0, 100], sap[IntegerDigits[#, 2]]>0&]

Crossrefs

Indices of positive 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.

Cf. A000120, A048793, A051293, A053632, A222955, A231204, A291166, A304818, A326672, A326673, A359043.

Sequence in context: A165947 A129517 A287061 * A161601 A352480 A031406

Adjacent sequences: A359398 A359399 A359400 * A359402 A359403 A359404

Keyword

nonn,base

Author

Gus Wiseman, Jan 05 2023

Status

approved