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.

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, 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, 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

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..93.

Wikipedia, Oppermann's conjecture.

Formula

floor(x^(phi^n)) = A382261(n) where x is this constant.

Example

1.5831204048581...

Crossrefs

Cf. A001622, A051021, A112597, A382261.

Sequence in context: A361221 A319261 A010489 * A378910 A196567 A200685

Adjacent sequences: A382257 A382258 A382259 * A382261 A382262 A382263

Keyword

nonn,cons

Author

Thomas Scheuerle, Mar 19 2025

Status

approved