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A169610
Numbers that are congruent to {5, 30} mod 37.
1
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
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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Dec 03 2009
EXTENSIONS
Added missing terms. Clarified the comment. - R. J. Mathar, Jul 07 2015
STATUS
approved