A364722 Numbers k that divide 1 + 2^m + 4^m for some m.
1, 3, 7, 13, 19, 21, 37, 39, 49, 57, 61, 67, 73, 79, 91, 97, 103, 109, 111, 139, 147, 151, 163, 169, 181, 183, 193, 199, 201, 211, 219, 237, 241, 271, 273, 291, 307, 309, 313, 327, 331, 337, 343, 349, 361, 367, 373, 379, 409, 417, 421, 427, 433, 453, 463, 469, 487, 489, 507, 523, 541, 543, 547
Offset: 1
Keywords
Examples
a(4) = 13 is a term because 1 + 2^4 + 4^4 = 273 = 21 * 13 is divisible by 13.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
filter:= proc(n) local x, r; for r in map(t -> subs(t,x), [msolve(1+x+x^2, n)]) do try NumberTheory:-ModularLog(r,2,n); catch "no solutions exist": next end try; return true od; false end proc: select(filter, [seq(i,i=1..1000,2)]); -
Python
from itertools import count, islice from sympy import sqrt_mod_iter, discrete_log def A364722_gen(startvalue=1): # generator of terms >= startvalue if startvalue <= 1: yield 1 if startvalue <= 3: yield 3 for k in count(max(startvalue,4)): for d in (r>>1 for r in sqrt_mod_iter(-3,k) if r&1): try: discrete_log(k,d,2) except: continue yield k break A364722_list = list(islice(A364722_gen(),20)) # Chai Wah Wu, May 02 2024
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