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A117606
a(n) = ones digit minus tens digit of the square of a(n-1), with a(0) = 2.
1
2, 4, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7, 5, 3, 9, -7
OFFSET
0,1
COMMENTS
From the 2006 Collaborative Problem Solving Contest, written by Tom Clymer. It repeats forever, obviously. If the terms are thought of as the absolute value of the difference of the digits, then the -7's should all be 7 instead, but the remaining terms are unchanged. (The original puzzle sequence had only 2,4,5,3,9 given).
LINKS
National Assessment and Testing, the sponsor of the contest from which this problem comes.
FORMULA
From Colin Barker, Oct 21 2017: (Start)
G.f.: (2 + 4*x + 5*x^2 + 3*x^3 + 7*x^4 - 11*x^5) / ((1 - x)*(1 + x)*(1 + x^2)).
a(n) = (5 + 9*(-1)^n + (2 - 5*i)*(-i)^n + (2+5*i)*i^n) / 2 for n>1.
a(n) = a(n-4) for n>6.
(End)
EXAMPLE
Since a(0) = 2, a(1) = 2^2 = 4 and since a(1) = 4, a(2) = the difference of the digits of 16 = 5.
PROG
(PARI) Vec((2 + 4*x + 5*x^2 + 3*x^3 + 7*x^4 - 11*x^5) / ((1 - x)*(1 + x)*(1 + x^2)) + O(x^100)) \\ Colin Barker, Oct 21 2017
CROSSREFS
Sequence in context: A026198 A026206 A353708 * A245814 A060736 A097292
KEYWORD
base,sign,easy
AUTHOR
Joshua Zucker, Apr 06 2006
STATUS
approved