OFFSET
1,2
COMMENTS
Every positive integer has a unique expression as a sum of distinct Jacobsthal numbers in which the index of the smallest summand is odd, with J(1) = 1 and J(2) = 1 both allowed. [Carlitz-Scoville-Hoggatt, 1972]. - Based on a comment in A001045 from Ira M. Gessel, Dec 31 2016.
The highest-order bits are on the left. Interpreting these as binary numbers we get A003159.
LINKS
Lars Blomberg, Table of n, a(n) for n = 1..10000
L. Carlitz, R. Scoville, and V. E. Hoggatt, Jr., Representations for a special sequence, Fibonacci Quarterly 10.5 (1972), 499-518, 550.
FORMULA
EXAMPLE
9 = 5+3+1 = J(4)+J(3)+J(1) = 1101.
MATHEMATICA
FromDigits[IntegerDigits[#, 2]] & /@ Select[Range[100], EvenQ[IntegerExponent[#, 2]] &] (* Amiram Eldar, Jul 14 2023 *)
PROG
(PARI) lista(kmax) = for(k = 1, kmax, if(!(valuation(k, 2)%2), print1(fromdigits(binary(k), 10), ", "))); \\ Amiram Eldar, Jul 14 2023
(Python)
from itertools import count, islice
def A280049_gen(): # generator of terms
return map(lambda n:int(bin(n)[2:]), filter(lambda n:(n&-n).bit_length()&1, count(1)))
CROSSREFS
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Dec 31 2016
EXTENSIONS
Corrected a(5), a(16) and more terms from Lars Blomberg, Jan 02 2017
STATUS
approved