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

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

Amiram Eldar, Table of n, a(n) for n = 0..43

Formula

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

Mathematica

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

Crossrefs

Cf. A000045, A000120, A011373.

Sequence in context: A324028 A373658 A097711 * A381141 A345104 A116434

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