

A100478


Pentanacci pi function: a(1)=a(2)=a(3)=a(4)=a(5)=1; for n>5, a(n)=pi(a(n1)+a(n2)+a(n3)+a(n4)+a(n5)) where pi = A000720.


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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
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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, kGeneralized Fibonacci numbers, Fib. Quart., 5 (1967), 258266.
V. E. Hoggatt, Jr. and M. Bicknell, Diagonal sums of generalized Pascal triangles, Fib. Quart., 7 (1969), 341358, 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(n1)+a(n2)+a(n3)+a(n4)+a(n5)).


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}] (* 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



