A364724 a(n) is the least k such that 1^k + 2^k + 4^k is divisible by A364722(n).

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

Offset: 1

Author

Robert Israel, Aug 04 2023

Keywords

• nonn
• look

Comments

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.

Examples

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

Links

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

Crossrefs

Cf. A001576, A364722.

Programs

Maple

f:= proc(n) local R,r,m,v;
   R:= map(t -> subs(t,x), [msolve(1+x+x^2, n)]);
   m:= infinity;
   for r in R do
     try
     v:= NumberTheory:-ModularLog(r,2,n);
     catch "no solutions exist": next
     end try;
     m:= min(m,v)
   od;
   subs(infinity=NULL,m);
end proc:
map(f, [seq(i,i=1..1000,2)]);

Python

from itertools import count, islice
from sympy import sqrt_mod_iter, discrete_log
def A364724_gen(): # generator of terms
    yield 0
    for k in count(2):
        m = None
        for d in sqrt_mod_iter(-3,k):
            r = d>>1 if d&1 else d+k>>1
            try:
                m = discrete_log(k,r,2) if m is None else min(m,discrete_log(k,r,2))
            except:
                continue
        if m is not None: yield m
A364724_list = list(islice(A364724_gen(),30))