login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A340956 Integers n such that s(n^2) = s(n)*(s(n)+1)/2, where s(n) is the sum of binary digits of n (A000120). 1
0, 1, 2, 4, 5, 8, 9, 10, 16, 17, 18, 20, 21, 32, 33, 34, 36, 37, 40, 42, 64, 65, 66, 68, 69, 72, 73, 74, 80, 81, 84, 128, 129, 130, 132, 133, 136, 137, 138, 144, 146, 148, 160, 161, 162, 168, 256, 257, 258, 260, 261, 264, 265, 266, 272, 273, 274, 276, 277, 288, 289, 292, 293, 296, 320, 321, 322, 324, 336, 337, 512, 513, 514, 516 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Also, integers n such that A159918(n) = A000217(A000120(n)).
For any n, s(n^2) <= s(n)*(s(n)+1)/2. This sequence gives n for which the equality is achieved.
LINKS
MAPLE
q:= n-> (s-> is(s(n^2)=(t->t(s(n)))(h->h*(h+1)/2)))(
k-> add(i, i=Bits[Split](k))):
select(q, [$0..555])[]; # Alois P. Heinz, Feb 01 2021
MATHEMATICA
s[n_] := DigitCount[n, 2, 1]; t[n_] := n*(n + 1)/2; Select[Range[0, 500], s[#^2] == t[s[#]] &] (* Amiram Eldar, Feb 01 2021 *)
PROG
(PARI) isok(n) = my(hn=hammingweight(n)); hammingweight(n^2) == hn*(hn+1)/2; \\ Michel Marcus, Feb 01 2021
CROSSREFS
Sequence in context: A359267 A279430 A003714 * A010402 A010443 A035269
KEYWORD
nonn,base
AUTHOR
Max Alekseyev, Feb 01 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 15:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)