A382261 -id:A382261 - 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.

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

Thomas Scheuerle, Mar 19 2025

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.

			1.5831204048581...

Wikipedia, Oppermann's conjecture.

Cf. A001622, A051021, A112597, A382261.

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

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.

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