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A168489 Numbers that are congruent to {7,11} mod 12. 5
7, 11, 19, 23, 31, 35, 43, 47, 55, 59, 67, 71, 79, 83, 91, 95, 103, 107, 115, 119, 127, 131, 139, 143, 151, 155, 163, 167, 175, 179, 187, 191, 199, 203, 211, 215, 223, 227, 235, 239, 247, 251, 259, 263, 271, 275, 283, 287, 295, 299, 307, 311, 319, 323, 331, 335 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Arkadiusz Wesolowski, Mar 16 2014: (Start)

Odd numbers m for which 2/m is not equal to 1/x + 1/y with x = 2*floor((m + 1)/4) + 1 and an integer y > x.

The primes together with 3 are in A002145. (End)

Odd numbers not of the form (4j+1)*3^k, {j,k>=0}. - Bob Selcoe, Aug 30 2015

Nonnegative k for which k == 3 (mod 4) and k^2 == 1 (mod 3). - Bruno Berselli, Apr 26 2018

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

FORMULA

a(n) = 12*n - a(n-1) - 6 for n>1, a(1)=7.

From R. J. Mathar, Mar 21 2010: (Start)

a(n) = 6*n - (-1)^n.

a(n) = a(n-1) + a(n-2) - a(n-3).

G.f.: x*(7 + 4*x + x^2)/ ((1+x) * (x-1)^2). (End)

E.g.f.: 1 + 6*x*exp(x) - exp(-x). - G. C. Greubel, Aug 30 2015

MATHEMATICA

LinearRecurrence[{1, 1, -1}, {7, 11, 19}, 60] (* or *) Select[Range[350],  MemberQ[{7, 11}, Mod[#, 12]]&] (* Harvey P. Dale, Nov 10 2011 *)

Rest[CoefficientList[Series[x (7 + 4 x + x^2)/((1 + x) (x - 1)^2), {x, 0, 56}], x] ] (* Ray Chandler, Jul 07 2015 *)

RecurrenceTable[{a[n] == 12 n - 6 - a[n-1], a[1]==7}, a, {n, 1, 100}] (* G. C. Greubel, Aug 30 2015 *)

PROG

(MAGMA) [6*n-(-1)^n: n in [1..60]]; // Vincenzo Librandi, Aug 10 2012

(PARI) x='x+O('x^100); Vec(x*(7+4*x+x^2)/((1+x)*(x-1)^2)) \\ Altug Alkan, Oct 22 2015

CROSSREFS

Cf. A239233.

Sequence in context: A195759 A130570 A106081 * A129899 A129842 A065312

Adjacent sequences:  A168486 A168487 A168488 * A168490 A168491 A168492

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Nov 27 2009

STATUS

approved

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Last modified August 15 16:48 EDT 2018. Contains 313778 sequences. (Running on oeis4.)