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%I #54 Apr 15 2023 04:21:33
%S 1,8,11,18,21,28,31,38,41,48,51,58,61,68,71,78,81,88,91,98,101,108,
%T 111,118,121,128,131,138,141,148,151,158,161,168,171,178,181,188,191,
%U 198,201,208,211,218,221,228,231,238,241,248,251,258,261,268,271,278,281,288,291,298,301,308,311,318,321
%N Numbers congruent to 1 or 8 mod 10.
%C A007310(a(n)+1) is always a multiple of 5.
%C a(1) = 1, a(n+1) = a(n)+7 when n is odd, a(n+1) = a(n)+3 when n is even.
%C a(n) mod 6 follows the following pattern: 1,2,5,0,3,4,1,2,5,0,3,4, and so on.
%C A020639(A007310(a(n)+1)) = 5.
%H Davis Smith, <a href="/A306277/b306277.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 5*n - 2*A000034(n+1).
%F a(n) = a(n-1) + a(n-2) - a(n-3) for n>3.
%F a(n) = A273669(n) - 1. - _Antti Karttunen_, Feb 07 2019
%F G.f.: x*(1 + 7*x + 2*x^2) / ((1 - x)^2*(1 + x)). - _Colin Barker_, Feb 09 2019
%F E.g.f.: 2 + (5*x - 3)*exp(x) + exp(-x). - _David Lovler_, Sep 07 2022
%F Sum_{n>=1} (-1)^(n+1)/a(n) = (5+sqrt(5))^(3/2)*phi*Pi/(100*sqrt(2)) + log(phi)/(2*sqrt(5)) + log(2)/5, where phi is the golden ratio (A001622). - _Amiram Eldar_, Apr 15 2023
%p seq(seq(10*i+j, j=[1, 8]), i=0..350);
%t Select[Range[350], MemberQ[{1, 8}, Mod[#, 10]] &]
%o (PARI) for(n=1, 350, if((n%10==1) || (n%10==8), print1(n, ", ")))
%o (PARI) Vec(x*(1 + 7*x + 2*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ _Colin Barker_, Feb 09 2019
%Y Cf. A001622, A020639, A007310, A000034.
%Y Cf. A017281, A017365 (bisections).
%Y One less than A273669.
%K nonn,easy,base
%O 1,2
%A _Davis Smith_, Feb 02 2019
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