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A318970
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a(1) = 3; for n > 1, a(n) = 2^(a(n-1) - 1) + 5.
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2
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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RecurrenceTable[{a[1]==3, a[n]==2^(a[n-1] - 1) + 5}, a, {n, 4}] (* Vincenzo Librandi, Sep 07 2018 *)
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PROG
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(Magma) [n le 1 select 3 else 2^(Self(n-1)-1)+5: n in [1..4]]; // Vincenzo Librandi, Sep 07 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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