

A316627


a(1)=2, a(2)=3; a(n) = a(n+1a(n1))+a(na(n2)) for n > 2.


1



2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 16, 17, 18, 18, 19, 20, 20, 20, 21, 22, 22, 23, 24, 24, 24, 24, 25, 26, 26, 27, 28, 28, 28, 29, 30, 30, 31, 32, 32, 32, 32, 32, 33, 34, 34, 35, 36, 36, 36, 37, 38, 38, 39, 40, 40, 40, 40, 41, 42, 42
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OFFSET

1,1


COMMENTS

This sequence increases slowly.
If k is not a power of 2, k occurs A001511(k) times. Otherwise, k occurs A001511(k)1 times.
This is the metaFibonacci sequence for s=1.


REFERENCES

B. W. Conolly, "MetaFibonacci sequences," in S. Vajda, editor, Fibonacci and Lucas Numbers and the Golden Section. Halstead Press, NY, 1989, pp. 127138. See Eq. (2).


LINKS

Nathan Fox, Table of n, a(n) for n = 1..10000


FORMULA

a(n+1)a(n)=1 or 0.
a(n)/n > C=1/2.


MAPLE

A316627:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 2: elif n = 2 then 3: else A316627(n + 1A316627(n1)) + A316627(nA316627(n2)): fi: end:


PROG

(MAGMA) I:=[2, 3]; [n le 2 select I[n] else Self(n+1Self(n1))+Self(nSelf(n2)): n in [1..100]]; // Vincenzo Librandi, Jul 09 2018
(GAP) a:=[2, 3];; for n in [3..75] do a[n]:=a[n+1a[n1]]+a[na[n2]]; od; a; # Muniru A Asiru, Jul 09 2018


CROSSREFS

Cf. A001511, A005185, A006949, A046699.
Sequence in context: A080444 A082288 A305397 * A099801 A099802 A196266
Adjacent sequences: A316624 A316625 A316626 * A316628 A316629 A316630


KEYWORD

nonn


AUTHOR

Nathan Fox, Jul 08 2018


STATUS

approved



