A301621 - OEIS

%I #19 Nov 27 2023 00:29:46

%S 11,29,47,83,101,119,137,173,191,209,227,263,281,299,317,353,371,389,

%T 407,443,461,479,497,533,551,569,587,623,641,659,677,713,731,749,767,

%U 803,821,839,857,893,911,929,947,983,1001,1019,1037,1073,1091,1109

%N Numbers not divisible by 2, 3 or 5 (A007775) with digital root 2.

%C Numbers congruent to 11, 29, 47, or 83 mod 90 with additive sum sequence 11 { + 18 + 18 + 36 + 18} {repeat ...}. Includes all prime numbers greater than 5 with digital root 2.

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

%F n == {11, 29, 47, 83} mod 90.

%F From _Colin Barker_, Mar 26 2018: (Start)

%F G.f.: x*(11 + 18*x + 18*x^2 + 36*x^3 + 7*x^4) / ((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)

%e 11+18=29; 29+18=47; 47+36=83; 83+18=101; 101+18=119.

%t Flatten[Table[90n - {79, 61, 43, 7}, {n, 30}]] (* _Alonso del Arte_, Mar 29 2018 *)

%o (PARI) Vec(x*(11 + 18*x + 18*x^2 + 36*x^3 + 7*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ _Colin Barker_, Mar 26 2018

%o (GAP) Filtered(Filtered([1..1200],n->n mod 2 <> 0 and n mod 3 <> 0 and n mod 5 <> 0),i->i-9*Int((i-1)/9)=2); # _Muniru A Asiru_, Apr 22 2018

%Y Intersection of A007775 and A017185.

%K nonn,base,easy

%O 1,1

%A _Gary Croft_, Mar 24 2018