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A220021 Number of cyclotomic cosets of 11 mod 10^n.

%I A220021 #28 Jul 03 2023 23:20:00
%S A220021 10,27,65,119,189,275,377,495,629,779,945,1127,1325,1539,1769,2015,
%T A220021 2277,2555,2849,3159,3485,3827,4185,4559,4949,5355,5777,6215,6669,
%U A220021 7139,7625,8127,8645,9179,9729,10295,10877,11475,12089,12719,13365,14027,14705,15399,16109,16835,17577,18335,19109,19899
%N A220021 Number of cyclotomic cosets of 11 mod 10^n.
%C A220021 How is this related to A181890? - _R. J. Mathar_, Apr 11 2013
%H A220021 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F A220021 Conjecture: a(n) = 8*n^2-2*n-1 for n>1. a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>4. G.f.: x*(5*x^3-14*x^2+3*x-10) / (x-1)^3. - _Colin Barker_, Apr 13 2013
%e A220021 a(2) = 27 because there are 27 cyclotomic cosets of 11 mod 100:
%e A220021 {1, 11, 21, 31, 41, 51, 61, 71, 81, 91}
%e A220021 {3, 33, 63, 93, 23, 53, 83, 13, 43, 73}
%e A220021 {7, 77, 47, 17, 87, 57, 27, 97, 67, 37}
%e A220021 {9, 99, 89, 79, 69, 59, 49, 39, 29, 19}
%e A220021 {2, 22, 42, 62, 82}
%e A220021 {12, 32, 52, 72, 92}
%e A220021 {4, 44, 84, 24, 64}
%e A220021 {14, 54, 94, 34, 74}
%e A220021 {6, 66, 26, 86, 46}
%e A220021 {16, 76, 36, 96, 56}
%e A220021 {8, 88, 68, 48, 28}
%e A220021 {18, 98, 78, 58, 38}
%e A220021 {5, 55}
%e A220021 {15, 65}
%e A220021 {25, 75}
%e A220021 {35, 85}
%e A220021 {45, 95}
%e A220021 {0}
%e A220021 {10}
%e A220021 {20}
%e A220021 {30}
%e A220021 {40}
%e A220021 {50}
%e A220021 {60}
%e A220021 {70}
%e A220021 {80}
%e A220021 {90}
%t A220021 a[n_] := DivisorSum[10^n, EulerPhi[#] / MultiplicativeOrder[11, #] &]; Array[a, 50] (* _Jean-François Alcover_, Dec 18 2015 *)
%o A220021 (PARI) for(n=1,50,print1(sumdiv(10^n, d, eulerphi(d)/znorder(Mod(11, d)))", "))
%Y A220021 Cf. A006694, A220468.
%K A220021 base,nonn
%O A220021 1,1
%A A220021 _V. Raman_, Jan 27 2013