A055872 - OEIS

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

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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 *)