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A301623 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 5. 1

%I

%S 23,41,59,77,113,131,149,167,203,221,239,257,293,311,329,347,383,401,

%T 419,437,473,491,509,527,563,581,599,617,653,671,689,707,743,761,779,

%U 797,833,851,869,887,923,941,959,977,1013,1031,1049,1067,1103,1121

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

%C Numbers == {23, 41, 59, 77} mod 90 with additive sum sequence 23{+18+18+18+36} {repeat ...}. Includes all primes number > 5 with digital root 5.

%H Colin Barker, <a href="/A301623/b301623.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 == {23, 41, 59, 77} mod 90.

%F From _Colin Barker_, Mar 25 2018: (Start)

%F G.f.: x*(23 + 18*x + 18*x^2 + 18*x^3 + 13*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 23+18=41; 41+18=59; 59+18=77; 77+36=113; 113+18=131.

%t LinearRecurrence[{1,0,0,1,-1},{23,41,59,77,113},50] (* _Harvey P. Dale_, Jul 28 2018 *)

%o (PARI) Vec(x*(23 + 18*x + 18*x^2 + 18*x^3 + 13*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ _Colin Barker_, Mar 25 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)=5); # _Muniru A Asiru_, Apr 22 2018

%Y Intersection of A007775 and A017221.

%K nonn,base,easy

%O 1,1

%A _Gary Croft_, Mar 24 2018

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Last modified January 28 22:40 EST 2020. Contains 331328 sequences. (Running on oeis4.)