|
|
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.
|
|
20
|
|
|
0, 1, 4, 9, 49, 81, 324, 2209, 15129, 25921, 103684, 710649, 4870849, 8346321, 33385284, 228826129, 1568397609, 2687489281, 10749957124, 73681302249, 505019158609, 865363202001, 3461452808004
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
Squares of A204520. The square roots of floor[a(n)/5] are given in A204521.
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
More terms added and offset changed to 1 by M. F. Hasler, Jan 15 2012
|
|
STATUS
|
approved
|
|
|
|