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A303296 Digital roots of fourth powers A000583. 0

%I

%S 1,7,9,4,4,9,7,1,9,1,7,9,4,4,9,7,1,9,1,7,9,4,4,9,7,1,9,1,7,9,4,4,9,7,

%T 1,9,1,7,9,4,4,9,7,1,9,1,7,9,4,4,9,7,1,9,1,7,9,4,4,9,7,1,9,1,7,9,4,4,

%U 9,7,1,9,1,7,9,4,4,9,7,1,9,1,7,9,4,4,9,7,1,9

%N Digital roots of fourth powers A000583.

%C This sequence is related to A056992, the digital roots of the squares, and also presents a period of 9, in this case repeat [1, 7, 9, 4, 4, 9, 7, 1, 9].

%C a(n) = 9 if n is a multiple of 3.

%C Replace 4 with 7 and 7 with 4 in A056992. - _Omar E. Pol_, Apr 21 2018

%H I. Izmirli, <a href="https://doi.org/10.4236/apm.2014.46039">On Some Properties of Digital Roots</a>, Advances in Pure Mathematics, Vol. 4 No. 6 (2014), Article ID:47285.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1).

%F a(n) = A010888(A000583(n)) = a(n - 9).

%t Table[FixedPoint[Total[IntegerDigits[#]] &, n^4], {n, 90}]

%o (PARI) a(n) = (n^4-1)%9+1; \\ _Michel Marcus_, Apr 22 2018

%Y Cf. A000583, A010888, A056992.

%K nonn,base,easy

%O 1,2

%A _Gaston Maire_ and students, Apr 21 2018

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Last modified May 19 20:41 EDT 2019. Contains 323410 sequences. (Running on oeis4.)