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
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
Programs
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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))
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