A055872 a(n) and floor(a(n)/8) are both squares; i.e., squares that remain squares when written in base 8 and last digit is removed.

0, 1, 4, 9, 36, 289, 1156, 9801, 39204, 332929, 1331716, 11309769, 45239076, 384199201, 1536796804, 13051463049, 52205852196, 443365544449, 1773462177796, 15061377048201, 60245508192804

Offset: 1

Author

Henry Bottomley, Jul 14 2000

Keywords

• base
• nonn
• easy

Comments

For the first 3 terms which have only 1 digit in base 8, removing this digit is meant to yield 0.

Base-8 analog of A055792 (base 2), A055793 (base 3), A055808 (base 4), A055812 (base 5), A055851 (base 6), A055859 (base 7), A204503 (base 9) and A023110 (base 10). - M. F. Hasler, Jan 15 2012

Examples

			a(5) = 289 because 289 = 17^2 = 441 base 8 and 44 base 8 = 36 = 6^2.
		

Links

• M. F. Hasler, Truncated squares, OEIS wiki, Jan 16 2012.
• Index to sequences related to truncating digits of squares.
• Index entries for linear recurrences with constant coefficients, signature (0,35,0,-35,0,1)

Crossrefs

Cf. A023110, A055792 (bisection).

Programs

Mathematica

Select[Range[0,8*10^6]^2,IntegerQ[Sqrt[FromDigits[Most[ IntegerDigits[ #,8]], 8]]]&] (* Harvey P. Dale, Aug 02 2016 *)

PARI

b=8;for(n=1,200,issquare(n^2\b) && print1(n^2,",")) \\ M. F. Hasler, Jan 15 2012

Formula

a(n) = A204514(n)^2. - M. F. Hasler, Jan 15 2012

Empirical g.f.: -x^2*(4*x+1)*(9*x^4-26*x^2+1) / ((x-1)*(x+1)*(x^2-6*x+1)*(x^2+6*x+1)). - Colin Barker, Sep 15 2014

Extensions

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