cp's OEIS Frontend

A382260 Decimal expansion of x, where x is the smallest number for which floor(x^(phi^k)) is prime for k > 0 where phi = (1+sqrt(5))/2, assuming that Oppermann's conjecture holds.

%I A382260 #24 Mar 28 2025 15:27:26
%S A382260 1,5,8,3,1,2,0,4,0,4,8,5,8,1,0,9,2,2,1,0,3,5,9,0,5,9,7,0,7,0,0,1,3,4,
%T A382260 5,4,0,3,1,1,0,5,4,9,6,0,6,4,1,7,9,3,7,8,6,3,7,6,2,8,2,8,8,6,1,9,2,8,
%U A382260 9,5,8,7,1,1,5,0,0,0,8,5,2,7,4,7,4,7,2,9,7,5,7,3,7
%N A382260 Decimal expansion of x, where x is the smallest number for which floor(x^(phi^k)) is prime for k > 0 where phi = (1+sqrt(5))/2, assuming that Oppermann's conjecture holds.
%C A382260 This constant can generate for all exponents k > 0 a prime number if the following conjecture is true: Let p be a prime > 2 and q = nexprime(p+1) then if there is always at least one prime inside the interval nextprime(p*q) to nextprime((p+1)*q)). But if this constant can generate prime numbers for all k, it is not directly a proof of this conjecture. If we would strengthen this further by omitting "nextprime" and allowing natural numbers for p and q, we will obtain essentially Oppermann's conjecture.
%H A382260 Wikipedia, <a href="https://en.wikipedia.org/wiki/Oppermann%27s_conjecture">Oppermann's conjecture</a>.
%F A382260 floor(x^(phi^n)) = A382261(n) where x is this constant.
%e A382260 1.5831204048581...
%Y A382260 Cf. A001622, A051021, A112597, A382261.
%K A382260 nonn,cons
%O A382260 1,2
%A A382260 _Thomas Scheuerle_, Mar 19 2025