A364724 - OEIS

%I #12 May 02 2024 14:29:33

%S 0,0,1,4,6,2,12,4,7,6,20,22,3,13,4,16,17,12,12,46,14,5,54,52,60,20,32,

%T 33,22,70,6,26,8,45,4,16,34,34,52,12,10,7,49,116,114,61,124,126,68,46,

%U 140,20,24,10,77,22,81,54,52,174,180,60,182,13,38,48,32,66,101,204,206,15,70,28,220

%N a(n) is the least k such that 1^k + 2^k + 4^k is divisible by A364722(n).

%C a(n) is the least k such that 1^k + 2^k + 4^k is divisible by the n-th number for which such k exists.

%H Robert Israel, <a href="/A364724/b364724.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 4 because A364722(4) = 13 and 1 + 2^4 + 4^4 = 273 = 21 * 13 is divisible by 13.

%p f:= proc(n) local R,r,m,v;

%p    R:= map(t -> subs(t,x), [msolve(1+x+x^2, n)]);

%p    m:= infinity;

%p    for r in R do

%p      try

%p      v:= NumberTheory:-ModularLog(r,2,n);

%p      catch "no solutions exist": next

%p      end try;

%p      m:= min(m,v)

%p    od;

%p    subs(infinity=NULL,m);

%p end proc:

%p map(f, [seq(i,i=1..1000,2)]);

%o (Python)

%o from itertools import count, islice

%o from sympy import sqrt_mod_iter, discrete_log

%o def A364724_gen(): # generator of terms

%o     yield 0

%o     for k in count(2):

%o         m = None

%o         for d in sqrt_mod_iter(-3,k):

%o             r = d>>1 if d&1 else d+k>>1

%o             try:

%o                 m = discrete_log(k,r,2) if m is None else min(m,discrete_log(k,r,2))

%o             except:

%o                 continue

%o         if m is not None: yield m

%o A364724_list = list(islice(A364724_gen(),30))

%Y Cf. A001576, A364722.

%K nonn,look

%O 1,4

%A _Robert Israel_, Aug 04 2023