

A316626


a(1)=a(2)=a(3)=1; a(n) = a(n2*a(n1))+a(n12*a(n2)) for n > 3.


1



1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20
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OFFSET

1,4


COMMENTS

This sequence increases slowly, and each term repeats at least three times.
If k is not a power of 2, then k appears in this sequence the same number of times as it appears in A081832. Otherwise, it appears exactly one additional time.


LINKS

Nathan Fox, Table of n, a(n) for n = 1..10000
A. Erickson, A. Isgur, B. W. Jackson, F. Ruskey and S. M. Tanny, Nested recurrence relations with Conollylike solutions, See Conjecture 5.1.


FORMULA

a(n+1)a(n)=1 or 0.
a(n)/n > C=1/4.


MAPLE

A316626:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 1: elif n = 3 then 1: else A316626(n2*A316626(n1)) + A316626(n12*A316626(n2)): fi: end:


PROG

(MAGMA) [n le 3 select 1 else Self(n2*Self(n1))+Self(n12*Self(n2)): n in [1..100]]; // Vincenzo Librandi, Jul 09 2018
(GAP) a:=[1, 1, 1];; for n in [4..80] do a[n]:=a[n2*a[n1]]+a[n12*a[n2]]; od; a; # Muniru A Asiru, Jul 09 2018


CROSSREFS

Cf. A005185, A046699, A081832.
Sequence in context: A068063 A087181 A034973 * A269734 A066927 A060065
Adjacent sequences: A316623 A316624 A316625 * A316627 A316628 A316629


KEYWORD

nonn


AUTHOR

Nathan Fox and Altug Alkan, Jul 08 2018


STATUS

approved



