cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A301623 #22 Jul 28 2018 15:14:43
%S A301623 23,41,59,77,113,131,149,167,203,221,239,257,293,311,329,347,383,401,
%T A301623 419,437,473,491,509,527,563,581,599,617,653,671,689,707,743,761,779,
%U A301623 797,833,851,869,887,923,941,959,977,1013,1031,1049,1067,1103,1121
%N A301623 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 5.
%C A301623 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 A301623 Colin Barker, <a href="/A301623/b301623.txt">Table of n, a(n) for n = 1..1000</a>
%H A301623 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A301623 Numbers == {23, 41, 59, 77} mod 90.
%F A301623 From _Colin Barker_, Mar 25 2018: (Start)
%F A301623 G.f.: x*(23 + 18*x + 18*x^2 + 18*x^3 + 13*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)).
%F A301623 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A301623 (End)
%e A301623 23+18=41; 41+18=59; 59+18=77; 77+36=113; 113+18=131.
%t A301623 LinearRecurrence[{1,0,0,1,-1},{23,41,59,77,113},50] (* _Harvey P. Dale_, Jul 28 2018 *)
%o A301623 (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 A301623 (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 A301623 Intersection of A007775 and A017221.
%K A301623 nonn,base,easy
%O A301623 1,1
%A A301623 _Gary Croft_, Mar 24 2018