A318970 -id:A318970 - cp's OEIS frontend

A318971 Primes that divide at least one term of A318970.

3, 29, 31821709567, 28480625878963

Offset: 1

Max Alekseyev, Sep 06 2018

No other terms below 10^14.
If prime p does not divide any of the first A227944(p) <= log_2(p) terms of A318970, then p does not divide any term of A318970, i.e., p does not belong to this sequence.
(2^260+5)/261 is a term (76-digit prime). Hence, a(5) <= (2^260+5)/261.
Any prime p with A318989(p)=0 belongs to this sequence. However, it is unknown if there is a term p with nonzero A318989(p).

			a(1)=3 divides A318970(k) for all k >= 1.
a(2)=29 divides A318970(k) for all k >= 3.
a(3)=31821709567 divides A318970(k) for all k >= 8.
a(4)=28480625878963 divides A318970(k) for all k >= 11.

Max Alekseyev, Iterations of 2^(n-1)+5: the strong law of small numbers, or something bigger?, MathOverflow, 2016.

Cf. A227944, A245594, A318970, A318989.

A318989 Limiting value of A318970(k) mod n as k grows.

Original entry on oeis.org

0, 1, 0, 1, 1, 3, 2, 5, 0, 1, 6, 9, 1, 9, 6, 5, 4, 9, 14, 1, 9, 17, 14, 21, 6, 1, 18, 9, 0, 21, 6, 5, 6, 21, 16, 9, 2, 33, 27, 21, 6, 9, 3, 17, 36, 37, 19, 21, 16, 31, 21, 1, 6, 45, 6, 37, 33, 29, 34, 21, 52, 37, 9, 5, 1, 39, 40, 21, 60, 51, 42, 45, 42, 39, 6, 33, 72, 27, 28, 21, 72, 47, 56, 9, 21, 3, 0, 61, 37, 81, 79, 37, 6, 19, 71, 69, 11, 65, 72, 81

Offset: 1

Max Alekseyev, Sep 06 2018

nonn

Is there a prime p in A318971 such that a(p) is nonzero?

Cf. A245970, A254410, A254411, A318970, A318971.

a(n) = A318970(k) mod n holds for any k >= A227944(n). In particular, a(n) = A318970(A227944(n)) mod n.

cp's OEIS Frontend

A318971 Primes that divide at least one term of A318970.

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