A056849 Final digit of n^n.

1, 4, 7, 6, 5, 6, 3, 6, 9, 0, 1, 6, 3, 6, 5, 6, 7, 4, 9, 0, 1, 4, 7, 6, 5, 6, 3, 6, 9, 0, 1, 6, 3, 6, 5, 6, 7, 4, 9, 0, 1, 4, 7, 6, 5, 6, 3, 6, 9, 0, 1, 6, 3, 6, 5, 6, 7, 4, 9, 0, 1, 4, 7, 6, 5, 6, 3, 6, 9, 0, 1, 6, 3, 6, 5, 6, 7, 4, 9, 0, 1, 4, 7, 6, 5, 6, 3, 6, 9, 0, 1, 6, 3, 6, 5, 6, 7, 4, 9, 0

Offset

1,2

Comments

Cyclic with a period of 20.

Also decimal expansion of 147656369016365674900/(10^20-1). - Bruno Berselli, Sep 27 2021

References

R. Euler and J. Sadek, "A Number That Gives The Units Of n^n", Journal of Recreational Mathematics, vol. 29(3), 1998, pp. 203-4.

Links

Table of n, a(n) for n=1..100.

Hung Viet Chu, New Transcendental Numbers from Certain Sequences, arXiv:1908.03855 [math.NT], 2019. Mentions this sequence.

Gregory P. Dresden, Three transcendental numbers from the last non-zero digits of n^n, F_n and n!, Mathematics Magazine, vol. 81, 2008, pp. 96-105.

Gregory Dresden, Two Irrational Numbers That Give the Last Non-Zero Digits of n! and n^n, arXiv:1904.10274 [math.NT], 2019.

Jose María Grau and A. M. Oller-Marcen, On the last digit and the last non-zero digit of n^n in base b, arXiv:1203.4066 [math.NT], 2012.

Jose María Grau and A. M. Oller-Marcen, On the last digit and the last non-zero digit of n^n in base b, Bull. Korean Math. Soc. 51 (2014), No. 5, pp. 1325-1337.

Index entries for sequences related to final digits of numbers

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

Maple

seq(n &^ n mod 10, n=1..120);

Mathematica

Table[PowerMod[n, n, 10], {n, 1, 100}]

Prog

(Magma) [Modexp(n, n, 10): n in [1..100]]; // Bruno Berselli, Sep 27 2021
(PARI) a(n)=lift(Mod(n, 10)^n) \\ Charles R Greathouse IV, Dec 29 2012
(Python)
def a(n): return pow(n, n, 10)
print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Sep 13 2022

Crossrefs

Cf. A000312, A061505, A116081.

n^n mod 3..9: A204688, A204689, A204690, A204671, A204693, A204694, A204695.

Sequence in context: A351547 A354828 A308366 * A116081 A361351 A275162

Adjacent sequences: A056846 A056847 A056848 * A056850 A056851 A056852

Keyword

nonn,base,easy

Author

Robert G. Wilson v, Aug 30 2000

Status

approved