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A258804 a(n) = gpf(a(n-3))*gpf(a(n-2)) + gpf(a(n-1)), with a(1)=a(2)=1 and a(3)=2 and where gpf(n) is the greatest prime dividing n, A006530. 1
1, 1, 2, 3, 5, 11, 26, 68, 160, 226, 198, 576, 1246, 122, 328, 5470, 3048, 22554, 69648, 24184, 262752, 4386396, 70190, 22222, 4639830, 1914046, 3227106, 35917950, 2738592, 325870, 124850, 8375086, 7397758, 129192, 6948110, 10496178, 82166, 740450, 44446188, 1473852, 184450, 342342, 14496, 740, 2906, 7040, 53772, 20464 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The sequence appears to oscillate about its mean, with greater amplitude each time (an empirical observation).

The sequence seems to always give a value for a(n) that is relative prime to each of g(n-1), g(n-2), and g(n-3), where g(i) = gpf(a(i)) (empirical observation).

Proof of the second observation: If a(n) is relatively prime to g(n-1), g(n-2), and g(n-3), then so is g(n). In particular, if g(n) is relatively prime to g(n-1) and g(n-2), then g(n-2)*g(n-1) + g(n) = a(n+1) is relatively prime to g(i) for i=n-2,n-1,n. - Danny Rorabaugh, Dec 01 2015

LINKS

Robert Israel, Table of n, a(n) for n = 1..80

EXAMPLE

Let gpf(x) = A006530(x).

a(4) = gpf(a(1))*gpf(a(2)) + gpf(a(3)) = 1*1 + 2 = 3.

a(5) = gpf(a(2))*gpf(a(3)) + gpf(a(4)) = 1*2 + 3 = 5.

MAPLE

gpf:= x -> max(numtheory:-factorset(x)):

gpf(1):= 1:

a:= proc(n) option remember;

  gpf(procname(n-3))*gpf(procname(n-2))+gpf(procname(n-1))

end proc:

a(1):= 1: a(2):= 1: a(3):=2:

seq(a(n), n=1..70); # Robert Israel, Dec 01 2015

PROG

(PARI) gpf(n) = if (n==1, 1, vecmax(factor(n)[, 1]));

lista(nn) = {print1(b = 1, ", "); print1(c = 1, ", "); print1(d = 2, ", "); for (n=1, nn, e = gpf(b)*gpf(c) + gpf(d); print1(e, ", "); b = c; c = d; d = e; ); } \\ Michel Marcus, Oct 07 2015

CROSSREFS

Cf. A006530.

Sequence in context: A076051 A000628 A273755 * A006888 A009589 A098179

Adjacent sequences:  A258801 A258802 A258803 * A258805 A258806 A258807

KEYWORD

nonn

AUTHOR

Iago Casabiell González, Sep 22 2015

STATUS

approved

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Last modified March 30 05:45 EDT 2020. Contains 333118 sequences. (Running on oeis4.)