A114477 Smallest Fibonacci number with Hamming weight n (i.e., smallest number with exactly n ones when written in binary), or -1 if no such number exists.

0, 1, 3, 13, 89, 55, 377, 1597, 987, 121393, 39088169, 28657, 514229, 3524578, 24157817, 1134903170, 102334155, 165580141, 701408733, 2504730781961, 956722026041, 1836311903, 139583862445, 6557470319842, 591286729879, 17167680177565, 4052739537881, 806515533049393

Offset

0,3

Comments

a(n) = MIN{A000045(k): A000120(A000045(k)) = n}.

Among the first 10^5 Fibonacci numbers, none have Hamming weight 44, 45, 61, 62, 76, 92, or 95. - T. D. Noe, Jun 25 2007

Links

Table of n, a(n) for n=0..27.

Mathematica

a[ n_ ] := Module[ {}, k = 0; While[ Not[ Plus @@ IntegerDigits[ Fibonacci[ k ]S, 2 ] == n ], k++ ]; Fibonacci[ k ] ]; Table[ a[ i ], {i, 0, 40} ] (* Stefan Steinerberger *)

Crossrefs

Sequence in context: A002725 A324028 A097711 * A345104 A116434 A174290

Adjacent sequences: A114474 A114475 A114476 * A114478 A114479 A114480

Keyword

nonn,base

Author

Jonathan Vos Post, Jun 24 2007

Extensions

Extended by Stefan Steinerberger, Jun 25 2007

Status

approved