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A082209 a(1) = 1, a(n) = smallest number such that the concatenation of a(n-1) and a(n) is a square. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..83.

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

FORMULA

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

a(n) = 1/6*{542*(n mod 6)-404*[(n+1) mod 6]-13*[(n+2) mod 6]+34*[(n+3) mod 6]+41*[(n+4) mod 6]+34*[(n+5) mod 6]} with n>=0. - Paolo P. Lava, Nov 27 2006

EXAMPLE

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

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 *)

PROG

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

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

CROSSREFS

Cf. A082210.

See A090566 for another version.

Sequence in context: A334445 A168198 A177898 * A264770 A143520 A075450

Adjacent sequences:  A082206 A082207 A082208 * A082210 A082211 A082212

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Apr 10 2003

EXTENSIONS

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

STATUS

approved

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Last modified July 28 03:49 EDT 2021. Contains 346316 sequences. (Running on oeis4.)