A260953 List of numbers of the forms (2^(4m+3)-3)/5 and (2^(12m+4)-3)/13 arranged in increasing order.

1, 1, 25, 409, 5041, 6553, 104857, 1677721, 20648881, 26843545, 429496729, 6871947673, 84577817521, 109951162777, 1759218604441, 28147497671065, 346430740566961, 450359962737049, 7205759403792793, 115292150460684697, 1418980313362273201, 1844674407370955161

Offset

1,3

Comments

This sequence is based on numbers (2^k-3) that are divisible by 5 or by 13, but not both. Its terms are (2^k-3)/5 when 2^k-3 is divisible by 5, and numbers (2^k-3)/13 when 2^k-3 is divisible by 13. [Comment clarified by Michel Marcus, Aug 06 2015]

For n>2, a(n) is of the form (2^(12*m+4)-3)/13 iff n == 1 (mod 4). - Bruno Berselli, Aug 07 2015

Links

Table of n, a(n) for n=1..22.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,4097,0,0,0,-4096).

Formula

From Bruno Berselli, Aug 07 2015: (Start)

G.f.: x*(1 + x + 25*x^2 + 409*x^3 + 944*x^4 + 2456*x^5 + 2432*x^6 + 2048*x^7)/((1 - x)*(1 + x)*(1 - 8*x)*(1 + 8*x)*(1 + 64*x^2)*(1 + x^2)).

a(n) = 4097*a(n-4) - 4096*a(n-8) for n>8. (End)

Example

a(4) = 409 = (2^(4*2+3)-3)/5, while a(5) = 5041 = (2^(12*1+4)-3)/13.

Mathematica

Take[Sort[Table[(2^(4 m + 3) - 3)/5, {m, 0, 15}]~Join~Table[(2^(12 m + 4) - 3)/13, {m, 0, 15}]], 22] (* Michael De Vlieger, Aug 06 2015 *)

Prog

(Magma) &cat [[(2^(12*m+4)-3)/13] cat [(2^(4*(3*m+i)+3)-3)/5: i in [0..2]]: m in [0..8]]; // Bruno Berselli, Aug 07 2015

Crossrefs

Sequence in context: A026391 A028044 A028057 * A025998 A024437 A028041

Adjacent sequences: A260950 A260951 A260952 * A260954 A260955 A260956

Keyword

nonn,easy

Author

Marco Ripà, Aug 05 2015

Status

approved