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A181866
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a(1) = 1, a(2) = 2. For n >= 3, a(n) is found by concatenating the fourth powers of the first n-1 terms of the sequence and then dividing the resulting number by a(n-1).
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9
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OFFSET
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1,2
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COMMENTS
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The calculations for the first few values of the sequence are
... 2^4 = 16 so a(3) = 116/2 = 58
... 58^4 = 11316496 so a(4) = 11611316496/58 = 200195112.
The value of a(6) is calculated in the Example section below.
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LINKS
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FORMULA
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DEFINITION
a(1) = 1, a(2) = 2, and for n >= 3
(1)... a(n) = concatenate(a(1)^4,a(2)^4,...,a(n-1)^4)/a(n-1).
RECURRENCE RELATION
For n >= 2
(2)... a(n+2) = a(n+1)^3 + (100^F(n,4))*a(n)
= a(n+1)^3 + (10^F(3*n))*a(n),
where F(n,4) is the Fibonacci polynomial F(n,x) evaluated at x = 4
and where F(n) denotes the n-th Fibonacci number A000045(n).
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EXAMPLE
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The recurrence relation (2) above gives
a(6) = a(5)^3+10^144*a(4)
= 200 19511 20000 00000 00000 00000 00000 00000 00000 00195 11200
00080 97251 90261 07158 64917 75226 28886 69453 43420 83613 55167
37330 42401 44438 01550 47183 94579 01959 53586 66752.
a(6) has 153 digits.
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MAPLE
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M:=5:
a:=array(1..M):s:=array(1..M):
a[1]:=1:a[2]:=2:
s[1]:=convert(a[1]^4, string):
s[2]:=cat(s[1], convert(a[2]^4, string)):
for n from 3 to M do
a[n] := parse(s[n-1])/a[n-1];
s[n]:= cat(s[n-1], convert(a[n]^4, string));
end do:
seq(a[n], n = 1..M);
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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STATUS
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approved
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