OFFSET
1,2
COMMENTS
It is shown in the Szalay reference that if y is a term of this sequence then y=7, y=23, or y=2^t+1 for some positive t. Also see the Bennett reference.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Michael A. Bennett, Perfect powers with few ternary digits, INTEGERS 12A (2012), #A3.
László Szalay, The equations 2^n+-2^m+-2^l=z^2, Indag. Math. 13 (2002) 131-142.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
a(n) = 3*a(n-1)-2*a(n-2) for n>9. - Colin Barker, Nov 06 2014
G.f.: x*(12*x^8-2*x^7-10*x^6+4*x^5-2*x^4-2*x^3-2*x^2+1) / ((x-1)*(2*x-1)). - Colin Barker, Nov 06 2014
MATHEMATICA
Select[Range[1, 1000000, 2], Total[IntegerDigits[#^2, 2]] <= 3 &] (* T. D. Noe, Dec 07 2012 *)
CoefficientList[Series[(12 x^8 - 2 x^7 - 10 x^6 + 4 x^5 - 2 x^4 - 2 x^3 - 2 x^2 + 1) / ((x - 1) (2 x - 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Nov 07 2014 *)
PROG
(PARI) is(n)=n%2 && hammingweight(n^2)<4 \\ Charles R Greathouse IV, Dec 10 2012
(PARI) Vec(x*(12*x^8-2*x^7-10*x^6+4*x^5-2*x^4-2*x^3-2*x^2+1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Nov 06 2014
(Magma) I:=[1, 3, 5, 7, 9, 17, 23, 33, 65, 129]; [n le 10 select I[n] else 3*Self(n-1)-2*Self(n-2): n in [1..50]]; // Vincenzo Librandi, Nov 07 2014
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
John W. Layman, Dec 07 2012
EXTENSIONS
Extended by T. D. Noe, Dec 07 2012
STATUS
approved