cp's OEIS Frontend

A283393 a(n) = gcd(n^2-1, n^2+9).

%I A283393 #34 Dec 12 2023 07:46:56
%S A283393 1,10,1,2,5,2,5,2,1,10,1,10,1,2,5,2,5,2,1,10,1,10,1,2,5,2,5,2,1,10,1,
%T A283393 10,1,2,5,2,5,2,1,10,1,10,1,2,5,2,5,2,1,10,1,10,1,2,5,2,5,2,1,10,1,10,
%U A283393 1,2,5,2,5,2,1,10,1,10,1,2,5,2,5,2,1,10,1,10,1,2,5,2,5,2,1,10
%N A283393 a(n) = gcd(n^2-1, n^2+9).
%C A283393 Periodic with period 10.
%C A283393 Similar sequences with formula gcd(n^2-1, n^2+k):
%C A283393 k= 1:  1,  2, 1, 2, 1,  2, 1,  2, 1,  2, 1,  2, 1, ...  (A000034)
%C A283393 k= 3:  1,  4, 1, 4, 1,  4, 1,  4, 1,  4, 1,  4, 1, ...  (A010685)
%C A283393 k= 5:  1,  6, 3, 2, 3,  6, 1,  6, 3,  2, 3,  6, 1, ...  (A129203, start 6)
%C A283393 k= 7:  1,  8, 1, 8, 1,  8, 1,  8, 1,  8, 1,  8, 1, ...  (A010689)
%C A283393 k= 9:  1, 10, 1, 2, 5,  2, 5,  2, 1, 10, 1, 10, 1, ...  (this sequence)
%C A283393 k=11:  1, 12, 3, 4, 3, 12, 1, 12, 3,  4, 3, 12, 1, ...  (A129197, start 12)
%C A283393 Connection between the values of a(n) and the last digit of n:
%C A283393 . if n ends with 0, 2 or 8, then a(n) = 1;
%C A283393 . if n ends with 1 or 9, then a(n) = 10;
%C A283393 . if n ends with 3, 5 or 7, then a(n) = 2;
%C A283393 . if n ends with 4 or 6, then a(n) = 5.
%C A283393 Also, continued fraction expansion of (57 + sqrt(4579))/114.
%H A283393 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1).
%F A283393 G.f.: (1 + 10*x + x^2 + 2*x^3 + 5*x^4 + 2*x^5 + 5*x^6 + 2*x^7 + x^8 + 10*x^9)/(1 - x^10).
%t A283393 Table[PolynomialGCD[n^2 - 1, n^2 + 9], {n, 0, 100}]
%t A283393 LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 10, 1, 2, 5, 2, 5, 2, 1, 10}, 100]
%o A283393 (Python) [1, 10, 1, 2, 5, 2, 5, 2, 1, 10]*10
%o A283393 (Sage) [gcd(n^2-1, n^2+9) for n in range(100)]
%o A283393 (Magma) &cat [[1, 10, 1, 2, 5, 2, 5, 2, 1, 10]^^10];
%o A283393 (Maxima) makelist(gcd(n^2-1, n^2+9), n, 0, 100);
%o A283393 (PARI) Vec((1 + 10*x + x^2 + 2*x^3 + 5*x^4 + 2*x^5 + 5*x^6 + 2*x^7 + x^8 + 10*x^9)/(1 - x^10) + O(x^100)) \\ _Colin Barker_, Mar 08 2017
%Y A283393 Cf. A000034, A010685, A010689, A129197, A129203.
%K A283393 nonn,easy
%O A283393 0,2
%A A283393 _Bruno Berselli_, Mar 07 2017