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A100478 Pentanacci pi function: a(1)=a(2)=a(3)=a(4)=a(5)=1; for n>5, a(n)=pi(a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5)) where pi = A000720. 0
1, 1, 1, 1, 1, 3, 4, 4, 6, 7, 9, 10, 11, 14, 15, 17, 19, 21, 23, 24, 27, 30, 30, 32, 34, 36, 37, 39, 40, 42, 44, 46, 47, 47, 48, 50, 51, 53, 53, 54, 55, 56, 58, 58, 60, 61, 62, 62, 62, 63, 63, 64, 65, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Based on the prime counting function pi(n) = number of primes less than or equal to n and similar to pentanacci sequence.

Starting with other values of a(1), a(2), a(3), a(4), a(5) what behaviors are possible? Does the sequence always stick at a single integer after some point, or can it go into a loop, or is there a third pattern?

REFERENCES

I. Flores, k-Generalized Fibonacci numbers, Fib. Quart., 5 (1967), 258-266.

V. E. Hoggatt, Jr. and M. Bicknell, Diagonal sums of generalized Pascal triangles, Fib. Quart., 7 (1969), 341-358, 393.

LINKS

Table of n, a(n) for n=1..73.

Andrew Booker, The Nth Prime Page.

Eric Weisstein's World of Mathematics, "Prime Counting Function."

FORMULA

a(1)=a(2)=a(3)=a(4)=a(5)=1; a(n) = pi(a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5)).

EXAMPLE

a(6) = pi(a(1)+a(2)+a(3)+a(4)+a(5)) = pi(1+1+1+1+1) = pi(5) = 3.

a(7) = pi(a(2)+a(3)+a(4)+a(5)+a(6)) = pi(1+1+1+1+3) = pi(7) = 4.

a(8) = pi(a(3)+a(4)+a(5)+a(6)+a(7)) = pi(1+1+1+3+4) = pi(10) = 4.

a(9) = pi(a(4)+a(5)+a(6)+a(7)+a(8)) = pi(1+1+3+4+4) = pi(13) = 6.

a(10) = pi(a(5)+a(6)+a(7)+a(8)+a(9)) = pi(1+3+4+4+6) = pi(18) = 7.

MATHEMATICA

a[1] = a[2] = a[3] = a[4] = a[5] = 1; a[n_] := a[n] = PrimePi[a[n - 1] + a[n - 2] + a[n - 3] + a[n - 4] + a[n - 5]]; Table[ a[n], {n, 53}] (from Robert G. Wilson v Dec 03 2004)

CROSSREFS

Cf. A001591, A038607.

Sequence in context: A117571 A008474 A111611 * A112376 A161359 A224212

Adjacent sequences:  A100475 A100476 A100477 * A100479 A100480 A100481

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Nov 22 2004

EXTENSIONS

Edited and extended by Robert G. Wilson v, Dec 03 2004

STATUS

approved

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Last modified April 20 01:48 EDT 2014. Contains 240777 sequences.