A055812 a(n) and floor(a(n)/5) are both squares; i.e., squares which remain squares when written in base 5 and last digit is removed.

0, 1, 4, 9, 49, 81, 324, 2209, 15129, 25921, 103684, 710649, 4870849, 8346321, 33385284, 228826129, 1568397609, 2687489281, 10749957124, 73681302249, 505019158609, 865363202001, 3461452808004

Offset: 1

Author

Henry Bottomley, Jul 14 2000

Keywords

• base
• nonn

Comments

For the first 3 terms, the above "base 5" interpretation is questionable, since they have only 1 digit in base 5. It is understood that dropping this digit yields 0. - M. F. Hasler, Jan 15 2012

Examples

			a(4) = 49 because 49 = 7^2 = 144 base 5 and 14 base 5 = 9 = 3^2.
		

Crossrefs

For analogs in other bases see A055792 (base 2), A055793 (base 3), A055808 (base 4), A055851 (base 6), A204517 (base 7), A204512 (base 8), A204503 (base 9) and A023110 (base 10).

Squares of A204520. The square roots of floor[a(n)/5] are given in A204521.

Programs

PARI

b=5;for(n=1,2e9,issquare(n^2\b) && print1(n^2,","))  \\ M. F. Hasler, Jan 15 2012

Formula

Empirical g.f.: -x^2*(9*x^11 +49*x^10 +324*x^9 +81*x^8 -698*x^7 -698*x^6 -968*x^5 -242*x^4 +49*x^3 +9*x^2 +4*x +1) / ((x -1)*(x +1)*(x^2 -4*x -1)*(x^2 +1)*(x^2 +4*x -1)*(x^4 +18*x^2 +1)). - Colin Barker, Sep 15 2014

Extensions

More terms added and offset changed to 1 by M. F. Hasler, Jan 15 2012