A082210 -id:A082210 - cp's OEIS frontend

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

Amarnath Murthy, Apr 10 2003

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

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

Cf. A082210.

See A090566 for another version.

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

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 *)

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

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

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

A090567 Squares arising in A082209.

Original entry on oeis.org

16, 64, 49, 961, 61504, 5041, 16, 64, 49, 961, 61504, 5041, 16, 64, 49, 961, 61504, 5041, 16, 64, 49, 961, 61504, 5041, 16, 64, 49, 961, 61504, 5041, 16, 64, 49, 961, 61504, 5041, 16, 64, 49, 961, 61504, 5041, 16, 64, 49, 961, 61504, 5041, 16, 64, 49

Offset: 1

Amarnath Murthy, Dec 11 2003

A090567(n)=[5041,16,64,49,961,61504][n%6+1] \\ M. F. Hasler, Nov 24 2015

a(n) = A082210(n+1)^2. - David Wasserman, Jan 05 2006

Corrected and extended by David Wasserman, Jan 05 2006

A264775 Square root of concatenation(A090566(n), A090566(n+1)).

Original entry on oeis.org

4, 25, 159, 531, 3101, 24903, 243740, 433129, 2703038, 21046245, 53478992, 292123372, 2164833445, 21425610902, 48888908358, 192151648872, 477890021223, 2279013856319, 19998940546342, 46961100477911, 72630984382646, 259140398165389, 1861711571434526, 14850553878036591, 56672657547446354, 303286443000496342, 2448230500494961492, 4821616822771036069, 24316253937847771953

Offset: 1

M. F. Hasler, Nov 24 2015

Sequence A090566 lists the smallest integer larger than the preceding term such that their concatenation is a square. This sequence lists the square root of these squares.
The initial term a(0)=1 corresponds to the natural extension A090566(0):=0 (or an "empty" A090566(0)).
Sequence A082210 is the analog of this corresponding to the variant A082209 of A090566.

David W. Wilson, Table of n, a(n) for n = 1..1839

Cf. A090566; A082210, A082209.

cp's OEIS Frontend

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

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A090567 Squares arising in A082209.

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A264775 Square root of concatenation(A090566(n), A090566(n+1)).

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