login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(1) = 1, a(n) = smallest number such that the concatenation of a(n-1) and a(n) is a square.
6

%I #30 Dec 14 2023 05:11:26

%S 1,6,4,9,61,504,1,6,4,9,61,504,1,6,4,9,61,504,1,6,4,9,61,504,1,6,4,9,

%T 61,504,1,6,4,9,61,504,1,6,4,9,61,504,1,6,4,9,61,504,1,6,4,9,61,504,1,

%U 6,4,9,61,504,1,6,4,9,61,504,1,6,4,9,61,504,1,6,4,9,61,504,1,6,4,9,61

%N a(1) = 1, a(n) = smallest number such that the concatenation of a(n-1) and a(n) is a square.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 1).

%F Periodic with period 6. - Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003

%e a(4) = 9 hence a(5) = 61 and 961 = 31^2.

%t PadRight[{},120,{1,6,4,9,61,504}] (* _Harvey P. Dale_, May 04 2013 *)

%t LinearRecurrence[{0, 0, 0, 0, 0, 1},{1, 6, 4, 9, 61, 504},83] (* _Ray Chandler_, Aug 26 2015 *)

%t CoefficientList[ Series[ (504x^5 + 61x^4 + 9x^3 + 4x^2 + 6x + 1)/(1 - x^6), {x, 0, 83}], x] (* _Robert G. Wilson v_, Nov 22 2015 *)

%o (Magma) &cat [[1,6,4,9,61,504]: n in [0..20]]; // _Vincenzo Librandi_, Nov 23 2015

%o (PARI) A082209(n)=[1, 6, 4, 9, 61, 504][(n-1)%6+1] \\ _M. F. Hasler_, Nov 24 2015

%Y Cf. A082210.

%Y See A090566 for another version.

%K base,nonn

%O 1,2

%A _Amarnath Murthy_, Apr 10 2003

%E Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003