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A055792 a(n) and floor(a(n)/2) are both squares; i.e. squares which remain squares when written in base 2 and last digit is removed. 32
0, 1, 9, 289, 9801, 332929, 11309769, 384199201, 13051463049, 443365544449, 15061377048201, 511643454094369, 17380816062160329, 590436102659356801, 20057446674355970889, 681362750825443653409, 23146276081390728245001, 786292024016459316676609 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) > 0 is a square such that a(n) - 1 is a product of powers. - Michel Lagneau, Feb 16 2012

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 0..654

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 (35,-35,1).

FORMULA

a(n) = 34*a(n-1) - a(n-2) - 16 = A001541(n-1)^2 = 2*A001542(n-1)^2 + 1 = 8*A001110(n-1) + 1.

a(n) = 35*a(n-1) - 35*a(n-2) + a(n-3) for n>3. G.f.: -x*(9*x^2-26*x+1) / ((x-1)*(x^2-34*x+1)). - Colin Barker, Sep 15 2014

a(n) = c*k^n + 1/2 + o(1) with k = 17+sqrt(288) = 33.97... and c = 17/4 - sqrt(18). - Charles R Greathouse IV, May 07 2015

a(n) = (4 + 2*(17+12*sqrt(2))^(1-n) + (34-24*sqrt(2))*(17+12*sqrt(2))^n)/8 for n>0. - Colin Barker, Mar 02 2016

EXAMPLE

a(2) = 9 because 9 = 3^2 = 1001 base 2 and 100 base 2 = 4 = 2^2.

PROG

(PARI) concat(0, Vec(-x*(9*x^2-26*x+1)/((x-1)*(x^2-34*x+1)) + O(x^100))) \\ Colin Barker, Sep 15 2014

(PARI) is(n)=issquare(n) && issquare(n\2) \\ Charles R Greathouse IV, May 07 2015

CROSSREFS

Cf. A023110, A247375.

Sequence in context: A110553 A078326 A118893 * A053935 A086699 A027834

Adjacent sequences:  A055789 A055790 A055791 * A055793 A055794 A055795

KEYWORD

nonn,base,easy

AUTHOR

Henry Bottomley, Jul 14 2000

STATUS

approved

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Last modified June 25 00:41 EDT 2017. Contains 288708 sequences.