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A260953 List of numbers of the forms (2^(4m+3)-3)/5 and (2^(12m+4)-3)/13 arranged in increasing order. 0
1, 1, 25, 409, 5041, 6553, 104857, 1677721, 20648881, 26843545, 429496729, 6871947673, 84577817521, 109951162777, 1759218604441, 28147497671065, 346430740566961, 450359962737049, 7205759403792793, 115292150460684697, 1418980313362273201, 1844674407370955161 (list; graph; refs; listen; history; text; internal format)
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

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)). [Bruno Berselli, Aug 07 2015]

a(n) = 4097*a(n-4) - 4096*a(n-8) for n>8. [Bruno Berselli, Aug 07 2015]

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

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Last modified January 25 10:03 EST 2022. Contains 350565 sequences. (Running on oeis4.)