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%I #66 Jun 01 2018 03:46:43
%S 17,53,71,89,107,143,161,179,197,233,251,269,287,323,341,359,377,413,
%T 431,449,467,503,521,539,557,593,611,629,647,683,701,719,737,773,791,
%U 809,827,863,881,899,917,953,971,989,1007,1043,1061,1079,1097,1133
%N Numbers not divisible by 2, 3 or 5 (A007775) with digital root 8.
%C Numbers == {17, 53, 71, 89} mod 90 with additive sum sequence 17{+36+18+18+18} {repeat ...}. Includes all prime numbers >5 with digital root 8.
%H Colin Barker, <a href="/A295869/b295869.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 Numbers == {17, 53, 71, 89} mod 90.
%F From _Colin Barker_, Mar 26 2018: (Start)
%F G.f.: x*(17 + 36*x + 18*x^2 + 18*x^3 + x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)).
%F a(n) = (5 + 9*(-1)^n - (9+9*i)*(-i)^n - (9-9*i)*i^n + 90*n) / 4, where i=sqrt(-1).
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F (End)
%e 17+36=53; 53+18=71; 71+18=89; 89+18=107; 107+36=143.
%p select(n->modp(n,2)<>0 and modp(n,3)<>0 and modp(n,5)<>0 and n-9*floor((n-1)/9)=8,[$1..1200]); # _Muniru A Asiru_, May 30 2018
%o (PARI) Vec(x*(17 + 36*x + 18*x^2 + 18*x^3 + x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ _Colin Barker_, Mar 26 2018
%o (GAP) Filtered([1..1200],n->n mod 2<>0 and n mod 3 <>0 and n mod 5<>0 and n-9*Int((n-1)/9)=8); # _Muniru A Asiru_, May 30 2018
%Y Intersection of A007775 and A017257.
%K nonn,base,easy
%O 1,1
%A _Gary Croft_, Mar 24 2018
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