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Final digit of prime(n).
(Formerly M0632)
57

%I M0632 #53 May 04 2024 11:55:58

%S 2,3,5,7,1,3,7,9,3,9,1,7,1,3,7,3,9,1,7,1,3,9,3,9,7,1,3,7,9,3,7,1,7,9,

%T 9,1,7,3,7,3,9,1,1,3,7,9,1,3,7,9,3,9,1,1,7,3,9,1,7,1,3,3,7,1,3,7,1,7,

%U 7,9,3,9,7,3,9,3,9,7,1,9,9,1,1,3,9,3,9,7,1,3,7,9,7,1,9,3,9,1,3,1,7,7,3,9,1

%N Final digit of prime(n).

%C Primes modulo 10.

%D Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.

%D Alberto Fraile et al., Prime numbers and random walks in a square grid, Phys. Rev. E 104, 054114 (2021)

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Nathaniel Johnston, <a href="/A007652/b007652.txt">Table of n, a(n) for n = 1..10000</a>

%H Milton Abramowitz and Irene A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H Evelyn Lamb, <a href="https://www.scientificamerican.com/article/peculiar-pattern-found-in-random-prime-numbers/">"Peculiar Pattern Found in 'Random' Prime Numbers"</a>, Nature, March 14, 2016, republished by Scientific American.

%H Robert J. Lemke Oliver and Kannan Soundararajan, <a href="https://arxiv.org/abs/1603.03720">Unexpected biases in the distribution of consecutive primes</a>, arXiv preprint arXiv:1603.03720 [math.NT], submitted on March 11, 2016.

%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>

%F a(n) = A010879(A000040(n)). - _Michel Marcus_, May 06 2014

%p seq(ithprime(n) mod 10, n=1..105); # _Nathaniel Johnston_, Jun 29 2011

%t Table[Mod[Prime[n], 10], {n, 120}] (* _Ray Chandler_, Oct 01 2005 *)

%t Mod[Prime[Range[100]], 10] (* _Vincenzo Librandi_, May 06 2014 *)

%o (Magma) [Intseq(p)[1]: p in PrimesUpTo(600)]; // _Bruno Berselli_, Feb 14 2013

%o (Magma) [p mod 10: p in PrimesUpTo(500)]; // _Vincenzo Librandi_, May 06 2014

%o (PARI) a(n)=prime(n)%10 \\ _Charles R Greathouse IV_, Oct 13 2016

%o (PARI) primes(100)%10 \\ _Charles R Greathouse IV_, Oct 13 2016

%Y Cf. A000040, A110923, A039701-A039706, A038194, A039709-A039715, A290450.

%K nonn,base,easy

%O 1,1

%A _N. J. A. Sloane_, _Simon Plouffe_

%E Extended by _Ray Chandler_, Oct 01 2005