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
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
- 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).
Crossrefs
Programs
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Magma
[Modexp(n, n, 10): n in [1..100]]; // Bruno Berselli, Sep 27 2021
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Maple
seq(n &^ n mod 10, n=1..120);
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Mathematica
Table[PowerMod[n, n, 10], {n, 1, 100}] -
PARI
a(n)=lift(Mod(n,10)^n) \\ Charles R Greathouse IV, Dec 29 2012
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Python
def a(n): return pow(n, n, 10) print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Sep 13 2022
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