login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A008935 If 2n = Sum 2^e(k) then a(n) = Sum e(k)^2. 4
1, 4, 5, 9, 10, 13, 14, 16, 17, 20, 21, 25, 26, 29, 30, 25, 26, 29, 30, 34, 35, 38, 39, 41, 42, 45, 46, 50, 51, 54, 55, 36, 37, 40, 41, 45, 46, 49, 50, 52, 53, 56, 57, 61, 62, 65, 66, 61, 62, 65, 66, 70, 71, 74, 75, 77, 78, 81, 82, 86, 87, 90, 91, 49, 50, 53, 54, 58, 59, 62 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

T. D. Noe, Table of n, a(n) for n=1..1023

FORMULA

G.f. 1/(1-x) * sum(k>=0, (k+1)^2*x^2^k/(1+x^2^k)). - Ralf Stephan, Jun 23 2003

EXAMPLE

To get a(5), we write 10 = 2+8 = 2^1 + 2^3 so a(5) = 1^2+3^2 = 10.

MATHEMATICA

a[n_] := Total[Flatten[Position[Reverse[IntegerDigits[n, 2]], 1]]^2]; Table[a[n], {n, 1, 70}] (* Jean-Fran├žois Alcover  Mar 21 2011 *)

PROG

(C): #include <stdio.h> #include <stdlib.h> #define USAGE "Usage: 'A008935 num'\n where num is the index of the desired ending value in the sequence.\n" #define MAX 1023 #define SHIFT_MAX 9

int main(int argc, char *argv[]) { unsigned short mask, i, j, end; unsigned long sum; if (argc < 2) { fprintf(stderr, USAGE); return EXIT_FAILURE; } end = atoi(argv[1]); end = (end >= MAX) ? MAX : end;

fprintf(stdout, "Values: "); for (i = 1; i <= end; i++) { sum = 0; mask = 1; for (j = 0; j < SHIFT_MAX; j++, mask *= 2) if (i & mask) sum += (j+1) * (j+1); fprintf(stdout, "%ld", sum); if (i < end) fprintf(stdout, ", "); } fprintf(stdout, "\n"); return EXIT_SUCCESS; }

(Haskell)

a008935 = f 1 where

   f k x | x == 0    = 0

         | r == 0    = f (k+1) x'

         | otherwise = k^2 + f (k+1) x' where (x', r) = divMod x 2

-- Reinhard Zumkeller, Jul 05 2011

CROSSREFS

Gives A003995 if sorted and duplicates removed.

Sequence in context: A064801 A109825 A193259 * A003995 A064473 A287962

Adjacent sequences:  A008932 A008933 A008934 * A008936 A008937 A008938

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Mar 22 2000

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 15 14:38 EDT 2019. Contains 327078 sequences. (Running on oeis4.)