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

1,3

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

Links

Table of n, a(n) for n=1..23.

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

Example

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

Prog

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

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.

Sequence in context: A115711 A029791 A053961 * A368337 A268099 A061867

Adjacent sequences: A055809 A055810 A055811 * A055813 A055814 A055815

Keyword

base,nonn

Author

Henry Bottomley, Jul 14 2000

Extensions

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

Status

approved