A318989 -id:A318989 - cp's OEIS frontend

A318970 a(1) = 3; for n > 1, a(n) = 2^(a(n-1) - 1) + 5.

3, 9, 261, 1852673427797059126777135760139006525652319754650249024631321344126610074238981

Offset: 1

Max Alekseyev, Sep 06 2018

nonn

a(n) divides a(n+1) for n <= 4, but it is unknown if this divisibility holds for larger n. In other words, it is unknown if this sequence is a subsequence of A245594.
Modulo any m > 1, the sequence stabilizes within the first A227944(m) <= log_2(m) terms. That is, for any n >= A227944(m), we have a(n) == a(A227944(m)) == A318989(m) (mod m).
It follows that the prime divisors of the terms (cf. A318971) are very sparse: if prime p does not divide any of the first log_2(p) terms, then p does not divide any term.

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

Cf. A245594, A318971, A318989.

[n le 1 select 3 else 2^(Self(n-1)-1)+5: n in [1..4]]; // Vincenzo Librandi, Sep 07 2018

RecurrenceTable[{a[1]==3, a[n]==2^(a[n-1] - 1) + 5}, a, {n, 4}] (* Vincenzo Librandi, Sep 07 2018 *)

A318971 Primes that divide at least one term of A318970.

Original entry on oeis.org

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.

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A318970 a(1) = 3; for n > 1, a(n) = 2^(a(n-1) - 1) + 5.

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A318971 Primes that divide at least one term of A318970.

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