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Numbers m == +- 2 (mod 10) but not m == 2 (mod 6).
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%I #30 Dec 26 2021 03:00:06

%S 12,18,22,28,42,48,52,58,72,78,82,88,102,108,112,118,132,138,142,148,

%T 162,168,172,178,192,198,202,208,222,228,232,238,252,258,262,268,282,

%U 288,292,298,312,318,322,328,342,348,352,358,372,378,382,388,402,408,412,418,432,438,442,448,462,468,472,478,492,498,502,508,522

%N Numbers m == +- 2 (mod 10) but not m == 2 (mod 6).

%C Also, numbers congruent to 12, 18, 22 or 28 (mod 30). Also, numbers such that A056619(n) = 5.

%H Colin Barker, <a href="/A280014/b280014.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F a(n+4) = a(n)+30.

%F From _Colin Barker_, Feb 12 2018: (Start)

%F G.f.: 2*x*(2 + x)*(3 + x^2 + x^3) / ((1 - x)^2*(1 + x)*(1 + x^2)).

%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

%F (End)

%F a(n) = (5 + 30*n - 3*(-1)^n + 10*A057077(n))/4. - _Stefano Spezia_, Dec 26 2021

%t Select[Range@ 524, MemberQ[{12, 18, 22, 28}, Mod[#, 30]] &] (* _Michael De Vlieger_, Feb 21 2017 *)

%t LinearRecurrence[{1,0,0,1,-1},{12,18,22,28,42},80] (* _Harvey P. Dale_, Nov 09 2017 *)

%o (PARI) a(n)=[12,18,22,28][(n-1)%4+1]+(n-1)\4*30

%o (PARI) Vec(2*x*(2 + x)*(3 + x^2 + x^3) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ _Colin Barker_, Feb 12 2018

%Y Cf. A056619, A057077.

%K nonn,easy

%O 1,1

%A _M. F. Hasler_, Feb 21 2017