A305380 Tribonacci representation of 2^n, written in base 10.

1, 2, 4, 9, 19, 41, 88, 195, 418, 1033, 2195, 4705, 10282, 21850, 49160, 104465, 223780, 550294, 1186344, 2525345, 5514438, 11817057, 26297040, 56201282, 138856076, 295217708, 632609378, 1382640428, 2974062096, 6603081730, 14149570820, 34976354857, 74361996963

Offset: 0

Author

N. J. A. Sloane, Jun 12 2018

Keywords

• nonn
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000

Crossrefs

Equals A003726(2^n).

Cf. A000073, A278038, A305876.

Programs

Maple

T:= proc(n) T(n):= (<<0|1|0>, <0|0|1>, <1|1|1>>^n)[2, 3] end:
b:= proc(n) option remember; local j;
      if n=0 then 0
    else for j from 2 while T(j+1)<=n do od;
         b(n-T(j))+2^(j-2)
      fi
    end:
a:= n-> b(2^n):
seq(a(n), n=0..35);  # Alois P. Heinz, Jun 12 2018

Python

def A305380(n):
    m, tlist, s = 2**n, [1,2,4], 0
    while tlist[-1]+tlist[-2]+tlist[-3] <= m:
        tlist.append(tlist[-1]+tlist[-2]+tlist[-3])
    for d in tlist[::-1]:
        s *= 2
        if d <= m:
            s += 1
            m -= d
    return s # Chai Wah Wu, Jun 12 2018

Extensions

a(9)-a(24) from Robert Israel, Jun 12 2018

Terms a(25) and beyond from Alois P. Heinz, Jun 12 2018