A169610 Numbers that are congruent to {5, 30} mod 37.

5, 30, 42, 67, 79, 104, 116, 141, 153, 178, 190, 215, 227, 252, 264, 289, 301, 326, 338, 363, 375, 400, 412, 437, 449, 474, 486, 511, 523, 548, 560, 585, 597, 622, 634, 659, 671, 696, 708, 733, 745, 770, 782, 807, 819, 844, 856, 881, 893, 918, 930, 955, 967, 992, 1004, 1029, 1041

Offset

1,1

Comments

For no term n of the sequence, 36*n^2+72*n+35 = (6*n+5)*(6*n+7) is of the form p*(p+2), where p and p+2 are primes.

The conjecture is evident, it can be proved as in A169599. - Bruno Berselli, Jan 07 2013

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) = (74*n+13*(-1)^n -41)/4 . - Bruno Berselli, Jan 05 2013

G.f.: x*(5+25*x+7*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 07 2015

Mathematica

Select[Range[1, 1200], MemberQ[{5, 30}, Mod[#, 37]]&] (* Harvey P. Dale, Sep 07 2012 *)
LinearRecurrence[{1, 1, -1}, {5, 30, 42}, 57] (* Ray Chandler, Jul 08 2015 *)
Rest[CoefficientList[Series[x*(5+25*x+7*x^2)/((1+x)*(x-1)^2), {x, 0, 57}], x]] (* Ray Chandler, Jul 08 2015 *)

Prog

(Magma) I:=[5, 30 , 42]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // Vincenzo Librandi, Jan 05 2013

Crossrefs

Sequence in context: A253805 A222463 A097252 * A206329 A043886 A044463

Adjacent sequences: A169607 A169608 A169609 * A169611 A169612 A169613

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 03 2009

Extensions

Added missing terms. Clarified the comment. - R. J. Mathar, Jul 07 2015

Status

approved