OFFSET
1,2
COMMENTS
Note that this sequence is a subsequence of A332416.
Prime q = m*2^(n + 2) + 1 does not divide ((F(n + 2) - 1)^m - 1)/(F(n + 2) - 2) if and only if q divides F(n + 2) - 2 = Product_{i = 0..n + 1} F(i). Direct implication is Theorem 2.26 of my article (see the links) and reciprocal implication is due to Wang (see A308695).
LINKS
Lorenzo Sauras Altuzarra, Some arithmetical problems that are obtained by analyzing proofs and infinite graphs, arXiv:2002.03075 [math.NT], 2020.
EXAMPLE
3 is a term of this sequence, because A(1,3) = A(2,2) = A(3,1) = 0.
MAPLE
A332414:=proc(n)
local c, i, k, q, r, v:
c:=0:
i:=0:
r:=1:
while c < n do
for k from 0 to r-1 do
q:=(k+1)*2^(r-k+2)+1:
if not isprime(q) or (2^(2^(r-k+2)) - 1) mod q != 0 then
i:=i+1:
fi:
od:
if i = r then
v:=r:
c:=c+1:
fi:
i:=0:
r:=r+1:
od:
return v:
end proc:
MATHEMATICA
Select[Range@ 29, NoneTrue[Transpose@ {#, Reverse@ #} &@ Range@ #, And[PrimeQ[#4], Mod[((#3 - 1)^#1 - 1)/(#3 - 2), #4] != 0] & @@ {#1, #2, 2^(2^(#2 + 2)) + 1, #1*2^(#2 + 2) + 1} & @@ # &] &] (* Michael De Vlieger, Feb 14 2020 *)
PROG
(PARI) isA(m, t) = ispseudoprime(q=4*m*2^t+1) && Mod(2, q)^(4*2^t)==1;
isok(r) = sum(i=1, r, isA(i, r-i+1)) == 0; \\ Jinyuan Wang, Feb 18 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Lorenzo Sauras Altuzarra, Feb 12 2020
EXTENSIONS
a(17)-a(67) from Jinyuan Wang, Feb 18 2020
STATUS
approved