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A317686 a(1) = a(2) = 1; for n >= 3, a(n) = a(t(n)) + a(n-t(n)) where t = A063882. 9
1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 11, 12, 12, 12, 13, 14, 15, 15, 16, 16, 17, 18, 19, 20, 20, 21, 21, 22, 22, 23, 24, 25, 26, 27, 27, 27, 27, 28, 29, 29, 30, 31, 32, 33, 33, 34, 35, 36, 36, 36, 37, 38, 38, 39, 40, 41, 41, 42, 42, 43, 44, 45, 46, 46, 47, 48, 49, 49, 49, 49, 50, 51 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This sequence hits every positive integer and it has a fractal-like structure, see scatterplot of 2*n-3*a(n) in Links section.

Let b(1) = b(2) = b(3) = b(4) = 1; for n >= 5, b(n) = b(t(n)) + b(n-t(n)) where t = A063882. Observe the symmetric relation between this sequence (a(n)) and b(n) thanks to plots of a(n)-2*n/3 and b(n)-n/3 in Links section. Note that a(n) + b(n) = n for n >= 2.

LINKS

Table of n, a(n) for n=1..77.

Altug Alkan, Scatterplot of 2*n-3*a(n) for n <= 36000

Altug Alkan, Scatterplots of a(n)-2*n/3 and b(n)-n/3 for n <= 36000

FORMULA

a(n+1) - a(n) = 0 or 1 for all n >= 1.

MAPLE

b:= proc(n) option remember; `if`(n<5, 1,

      b(n-b(n-1)) +b(n-b(n-4)))

    end:

a:= proc(n) option remember; `if`(n<3, 1,

      a(b(n)) +a(n-b(n)))

    end:

seq(a(n), n=1..100);  # Alois P. Heinz, Aug 05 2018

PROG

(PARI) t=vector(99); t[1]=t[2]=t[3]=t[4]=1; for(n=5, #t, t[n] = t[n-t[n-1]]+t[n-t[n-4]]); a=vector(99); a[1]=a[2]=1; for(n=3, #a, a[n] = a[t[n]]+a[n-t[n]]); a

CROSSREFS

Cf. A063882, A317648.

Sequence in context: A194640 A189726 A093878 * A156689 A168052 A131737

Adjacent sequences:  A317683 A317684 A317685 * A317687 A317688 A317689

KEYWORD

nonn

AUTHOR

Altug Alkan, Aug 04 2018

STATUS

approved

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Last modified June 21 19:12 EDT 2021. Contains 345365 sequences. (Running on oeis4.)