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

Author

Henry Bottomley, Jul 14 2000

Keywords

• base
• nonn

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

Examples

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

Links

• M. F. Hasler, Truncated squares, OEIS wiki, Jan 16 2012
• Index to sequences related to truncating digits of squares.

Crossrefs

Cf. A023110.

Programs

PARI

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

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

Extensions

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