A093069 a(n) = (2^n + 1)^2 - 2.

7, 23, 79, 287, 1087, 4223, 16639, 66047, 263167, 1050623, 4198399, 16785407, 67125247, 268468223, 1073807359, 4295098367, 17180131327, 68720001023, 274878955519, 1099513724927, 4398050705407, 17592194433023, 70368760954879, 281475010265087, 1125899973951487

Offset

1,1

Comments

Cletus Emmanuel calls these "Kynea numbers".

Difference between the smallest digitally balanced number with 2n+4 binary digits and the largest digitally balanced number with 2n+2 binary digits (see A031443): 7 = 9-2 = 1001-10, 23 = 35-12 = 100011-1100, 79 = 135-56 = 10000111-111000 etc. - Juri-Stepan Gerasimov, Jun 01 2011

Links

Michael De Vlieger, Table of n, a(n) for n = 1..1660

Amelia Carolina Sparavigna, Binary Operators of the Groupoids of  OEIS A093112 and A093069 Numbers(Carol and Kynea Numbers), Department of Applied Science and Technology, Politecnico di Torino (Italy, 2019).

Amelia Carolina Sparavigna, Some Groupoids and their Representations by Means of Integer Sequences, International Journal of Sciences (2019) Vol. 8, No. 10.

Eric Weisstein's World of Mathematics, Near-Square Prime

Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Formula

a(n) = 4^n+2^(n+1)-1.

G.f.: -x*(7-26*x+16*x^2) / ( (x-1)*(2*x-1)*(4*x-1) ). - R. J. Mathar, Jun 01 2011

a(n) = A092431(n+2) - A020522(n+1). - R. J. Mathar, Jun 01 2011

E.g.f.: -exp(x) + 2*exp(2*x) + exp(4*x) - 2. - Stefano Spezia, Dec 09 2019

Example

G.f. = 7*x + 23*x^2 + 79*x^3 + 287*x^4 + 1087*x^5 + 4223*x^6 + 16639*x^7 + ...

Maple

A093069:=n->(2^n+1)^2-2: seq(A093069(n), n=1..30);

Mathematica

a[ n_] := If[ n < 1, 0, 4^n + 2^(n + 1) - 1]; (* Michael Somos, Jul 08 2014 *)
CoefficientList[Series[(7 - 26*x + 16*x^2)/((1 - x)*(2*x - 1)*(4*x - 1)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jul 08 2014 *)

Prog

(PARI) vector(100, n, (2^n+1)^2-2) \\ Colin Barker, Jul 08 2014
(PARI) Vec(-(16*x^2-26*x+7)/((x-1)*(2*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Jul 08 2014
(Magma) [(2^n+1)^2-2 : n in [1..30]]; // Wesley Ivan Hurt, Jul 08 2014

Crossrefs

Cf. A091514 (primes of the form (2^n + 1)^2 - 2).

Cf. A244663.

Sequence in context: A018886 A145842 A086908 * A341665 A322269 A303890

Adjacent sequences: A093066 A093067 A093068 * A093070 A093071 A093072

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 17 2004

Extensions

More terms from Colin Barker, Jul 08 2014

Status

approved