A082209 a(1) = 1, a(n) = smallest number such that the concatenation of a(n-1) and a(n) is a square.

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, 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, 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

Offset: 1

Author

Amarnath Murthy, Apr 10 2003

Keywords

• base
• nonn

Examples

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

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A082210.

See A090566 for another version.

Programs

Magma

&cat [[1,6,4,9,61,504]: n in [0..20]]; // Vincenzo Librandi, Nov 23 2015

Mathematica

PadRight[{},120,{1,6,4,9,61,504}] (* Harvey P. Dale, May 04 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 1},{1, 6, 4, 9, 61, 504},83] (* Ray Chandler, Aug 26 2015 *)
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 *)

PARI

A082209(n)=[1, 6, 4, 9, 61, 504][(n-1)%6+1] \\ M. F. Hasler, Nov 24 2015

Formula

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

Extensions

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