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A303296
Digital roots of fourth powers A000583.
1
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, 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, 9, 7, 1, 9, 1, 7, 9, 4, 4, 9, 7, 1, 9, 1, 7, 9, 4, 4, 9, 7, 1, 9
OFFSET
1,2
COMMENTS
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].
a(n) = 9 if n is a multiple of 3.
Replace 4 with 7 and 7 with 4 in A056992. - Omar E. Pol, Apr 21 2018
a(n) is also the decimal expansion of 598165730/333333333. - Enrique Pérez Herrero, Nov 13 2021
LINKS
I. Izmirli, On Some Properties of Digital Roots, Advances in Pure Mathematics, Vol. 4 No. 6 (2014), Article ID:47285.
FORMULA
a(n) = A010888(A000583(n)) = a(n - 9).
MATHEMATICA
Table[FixedPoint[Total[IntegerDigits[#]] &, n^4], {n, 90}]
PROG
(PARI) a(n) = (n^4-1)%9+1; \\ Michel Marcus, Apr 22 2018
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Gaston Maire and students, Apr 21 2018
STATUS
approved