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

1,4

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.

Links

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

Example

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

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)]);

Prog

(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))

Crossrefs

Cf. A001576, A364722.

Sequence in context: A256508 A059030 A066984 * A241341 A085595 A173458

Adjacent sequences: A364721 A364722 A364723 * A364725 A364726 A364727

Keyword

nonn,look

Author

Robert Israel, Aug 04 2023

Status

approved