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Digital roots of A057084.
0

%I #48 Jul 06 2024 10:30:31

%S 1,8,2,6,5,1,4,6,7,8,8,9,8,1,7,3,4,8,5,3,2,1,1,9,1,8,2,6,5,1,4,6,7,8,

%T 8,9,8,1,7,3,4,8,5,3,2,1,1,9,1,8,2,6,5,1,4,6,7,8,8,9,8,1,7,3,4,8,5,3,

%U 2,1,1

%N Digital roots of A057084.

%C Periodic with period 24. The cycle is in reverse order to that of the digital roots of the Fibonacci numbers (A030132).

%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

%F a(n) = A010888(A041025(n)) for n > 0.

%F a(n) = A010888(A057084(n)) for n > 0.

%F a(n) = A010888(A015454(n+3)) for n > 0.

%F a(n) = A010888(A114479(n+5)) for n > 0.

%F a(n) = A010888(A164546(n+3)) for n > 0.

%F a(n) = A030132(24 - (n mod 24)). - _Filip Zaludek_, Dec 09 2018

%t digRoot[n_]:=FixedPoint[Total[IntegerDigits[#, 10]] &, n] ; digRoot/@LinearRecurrence[{8, -8}, {1, 8}, 100] (* _Amiram Eldar_, Nov 29 2018 *)

%o (GAP) A057084:=[1,8];; for n in [3..80] do A057084[n]:=8*(A057084[n-1]-A057084[n-2]);; od; a:=List(A057084,i->1+(i-1) mod 9); # _Muniru A Asiru_, Nov 29 2018

%Y Cf. A010888 (digital root), A057084, A030132 (order of cycle digits reversed), A000045, A015454, A041025, A114479, A164546.

%K nonn,base,easy

%O 1,2

%A _Ondrej Janicko_, Nov 27 2018