A168489 Numbers that are congruent to {7,11} mod 12.

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

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

Numbers that are not divisible by their digital root in base 5. - Amiram Eldar, Nov 24 2022

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

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/12 - log(2+sqrt(3))/(2*sqrt(3)). - Amiram Eldar, Dec 30 2021

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. A002145, A239233.

Sequence in context: A130570 A106081 A329857 * A329979 A129899 A129842

Adjacent sequences: A168486 A168487 A168488 * A168490 A168491 A168492

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 27 2009

Status

approved