A348368 Numbers k such that w(k + w(k)) < w(k), where w(k) is the binary weight of k, A000120(k).

6, 7, 13, 14, 15, 21, 29, 30, 31, 37, 45, 46, 47, 55, 59, 60, 61, 62, 63, 69, 77, 78, 79, 87, 91, 92, 93, 94, 95, 103, 107, 108, 109, 111, 115, 123, 124, 125, 126, 127, 133, 141, 142, 143, 151, 155, 156, 157, 158, 159, 167, 171, 172, 173, 175, 179, 187, 188, 189

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

k : A000120(A092391(k)) < A000120(k); A348367(k) < A000120(k).

Example

k = 91; A000120(91 + A000120(91)) < A000120(91), thus k = 91 is a term.

Maple

q:= n-> (wt-> is(wt(n+wt(n))<wt(n)))(k-> add(i, i=Bits[Split](k))):
select(q, [$0..200])[];  # Alois P. Heinz, Oct 15 2021

Mathematica

h[n_] := DigitCount[n, 2, 1]; q[n_] := h[n + (hn = h[n])] < hn; Select[Range[200], q] (* Amiram Eldar, Oct 15 2021 *)

Prog

(Python)
def h(n): return bin(n).count('1')
def ok(n): return h(n + h(n)) < h(n)
print(list(filter(ok, range(1, 190)))) # Michael S. Branicky, Oct 15 2021

Crossrefs

Cf. A000120, A092391, A348367.

Sequence in context: A331860 A069198 A069136 * A277137 A047335 A182623

Adjacent sequences: A348365 A348366 A348367 * A348369 A348370 A348371

Keyword

nonn,base,easy

Author

Ctibor O. Zizka, Oct 15 2021

Status

approved