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

%I A131097 #17 Feb 16 2025 08:33:06
%S A131097 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,
%T A131097 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,
%U A131097 6,4,10,2,8,4,10,4,10,1,4,4,8,2,8,6,16,4,10,2,8,4,10,4
%N A131097 Sum of digits of 3-smooth numbers in ternary representation.
%C A131097 a(n) = A053735(A003586(n)); values are even iff greater than 1.
%H A131097 Robert Israel, <a href="/A131097/b131097.txt">Table of n, a(n) for n = 1..10000</a>
%H A131097 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DigitSum.html">Digit Sum</a>
%H A131097 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Ternary.html">Ternary</a>
%p A131097 Res:= NULL: N:= 10^6:
%p A131097 for a from 0 to ilog2(N) do
%p A131097   for b from 0 do
%p A131097     v:= 2^a*3^b;
%p A131097     if v > N then break fi;
%p A131097     Res:= Res, v;
%p A131097 od od:
%p A131097 TS:= sort([Res]):
%p A131097 map(t -> convert(convert(t,base,3),`+`), TS); # _Robert Israel_, Oct 08 2018
%o A131097 (Python)
%o A131097 from sympy import integer_log
%o A131097 from sympy.ntheory import digits
%o A131097 def A131097(n):
%o A131097     def bisection(f,kmin=0,kmax=1):
%o A131097         while f(kmax) > kmax: kmax <<= 1
%o A131097         kmin = kmax >> 1
%o A131097         while kmax-kmin > 1:
%o A131097             kmid = kmax+kmin>>1
%o A131097             if f(kmid) <= kmid:
%o A131097                 kmax = kmid
%o A131097             else:
%o A131097                 kmin = kmid
%o A131097         return kmax
%o A131097     def f(x): return n+x-sum((x//3**i).bit_length() for i in range(integer_log(x,3)[0]+1))
%o A131097     return sum(digits(bisection(f,n,n),3)[1:]) # _Chai Wah Wu_, Jan 31 2025
%K A131097 nonn,base,look
%O A131097 1,2
%A A131097 _Reinhard Zumkeller_, Jun 14 2007