A055851 a(n) and floor(a(n)/6) are both squares; i.e., squares that remain squares when written in base 6 and last digit is removed.

0, 1, 4, 9, 25, 100, 729, 2401, 9604, 71289, 235225, 940900, 6985449, 23049601, 92198404, 684502569, 2258625625, 9034502500, 67074266169, 221322261601, 885289046404, 6572593581849, 21687323011225, 86749292044900

Offset

1,3

Comments

For the first 3 terms, the above "base 6" interpretation is questionable, since they have only 1 digit in base 6. It is understood that dropping this digit yields 0. - M. F. Hasler, Jan 15 2012

Base-6 analog of A055792 (base 2), A055793 (base 3), A055808 (base 4), A055812 (base 5), A204517 (base 7), A204503 (base 9) and A023110 (base 10). - M. F. Hasler, Jan 15 2012

Links

Table of n, a(n) for n=1..24.

M. F. Hasler, Truncated squares, OEIS wiki, Jan 16 2012

Index to sequences related to truncating digits of squares.

Formula

a(n) = A204518(n)^2. - M. F. Hasler, Jan 15 2012

Empirical g.f.: -x^2*(9*x^8+100*x^7+25*x^6-162*x^5-296*x^4-74*x^3+9*x^2+4*x+1) / ((x-1)*(x^2+x+1)*(x^6-98*x^3+1)). - Colin Barker, Sep 15 2014

Example

a(5) = 100 because 100 = 10^2 = 244 base 6 and 24 base 6 = 16 = 4^2.

Prog

(PARI) b=6; for(n=1, 2e9, issquare(n^2\b) & print1(n^2, ", ")) \\ M. F. Hasler, Jan 15 2012

Crossrefs

Cf. A023110.

Sequence in context: A117678 A167045 A262753 * A025494 A087374 A081948

Adjacent sequences: A055848 A055849 A055850 * A055852 A055853 A055854

Keyword

base,nonn

Author

Henry Bottomley, Jul 14 2000

Extensions

More terms added and offset changed to 1 by M. F. Hasler, Jan 16 2012

Status

approved