OFFSET
0,2
COMMENTS
Clearly every positive integer appears at least once in this sequence.
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..11264
FORMULA
a(n) = the least k such that A000788(k) > n. - Antti Karttunen, Jun 20 2014
Sum_{n>=1} (-1)^(n+1)/a(n) = Sum_{n>=1} (-1)^(n+1)/A000069(n) = 0.67968268... . - Amiram Eldar, Feb 18 2024
EXAMPLE
The binary representation of 16 is 10000, which has one 1-bit (and four 0-bits), hence 16 appears once in this sequence (and four times in A100921).
MAPLE
T:= n-> n$add(i, i=Bits[Split](n)):
seq(T(n), n=1..30); # Alois P. Heinz, Nov 11 2024
MATHEMATICA
Table[Table[n, DigitCount[n, 2, 1]], {n, 30}]//Flatten (* Harvey P. Dale, Aug 31 2017 *)
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(Python)
def A000788(n): return (n+1)*n.bit_count()+(sum((m:=1<<j)*((k:=n>>j)-(r if n<<1>=m*(r:=k<<1|1) else 0)) for j in range(1, n.bit_length()+1))>>1)
def A100922(n):
if n == 0: return 1
m, k = 1, 1
while A000788(m)<=n: m<<=1
while m-k>1:
r = m+k>>1
if A000788(r)>n:
m = r
else:
k = r
return m # Chai Wah Wu, Nov 11 2024
CROSSREFS
KEYWORD
base,easy,nonn,tabf
AUTHOR
Rick L. Shepherd, Nov 21 2004
STATUS
approved