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

1,3

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

Links

Table of n, a(n) for n=1..21.

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)

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A023110, A055792 (bisection).

Sequence in context: A176830 A077211 A073977 * A066924 A251689 A249101

Adjacent sequences: A055869 A055870 A055871 * A055873 A055874 A055875

Keyword

base,nonn,easy

Author

Henry Bottomley, Jul 14 2000

Extensions

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

Status

approved