A131097 Sum of digits of 3-smooth numbers in ternary representation.

1, 2, 1, 2, 2, 4, 1, 2, 4, 2, 4, 1, 4, 2, 4, 2, 4, 4, 1, 4, 2, 6, 4, 2, 4, 4, 1, 4, 4, 2, 6, 4, 2, 8, 4, 4, 1, 4, 4, 2, 8, 6, 4, 2, 8, 4, 4, 10, 1, 4, 4, 2, 8, 6, 4, 10, 2, 8, 4, 4, 10, 1, 4, 4, 8, 2, 8, 6, 4, 10, 2, 8, 4, 10, 4, 10, 1, 4, 4, 8, 2, 8, 6, 16, 4, 10, 2, 8, 4, 10, 4

Offset

1,2

Comments

a(n) = A053735(A003586(n)); values are even iff greater than 1.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Digit Sum

Eric Weisstein's World of Mathematics, Ternary

Maple

Res:= NULL: N:= 10^6:
for a from 0 to ilog2(N) do
  for b from 0 do
    v:= 2^a*3^b;
    if v > N then break fi;
    Res:= Res, v;
od od:
TS:= sort([Res]):
map(t -> convert(convert(t, base, 3), `+`), TS); # Robert Israel, Oct 08 2018

Prog

(Python)
from sympy import integer_log
from sympy.ntheory import digits
def A131097(n):
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = kmax >> 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return n+x-sum((x//3**i).bit_length() for i in range(integer_log(x, 3)[0]+1))
    return sum(digits(bisection(f, n, n), 3)[1:]) # Chai Wah Wu, Jan 31 2025

Crossrefs

Sequence in context: A336138 A366600 A365461 * A218666 A062790 A046640

Adjacent sequences: A131094 A131095 A131096 * A131098 A131099 A131100

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Jun 14 2007

Status

approved