A303296 Digital roots of fourth powers A000583.

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

Author

Gaston Maire and students, Apr 21 2018

Keywords

• nonn
• base
• easy

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.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A000583, A010888, A056992.

Programs

Mathematica

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

PARI

a(n) = (n^4-1)%9+1; \\ Michel Marcus, Apr 22 2018

Formula

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