A007652 Final digit of prime(n). (Formerly M0632)

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, 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, 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

Offset

1,1

Comments

Primes modulo 10.

References

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.

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

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Alberto Fraile et al., Prime numbers and random walks in a square grid, Phys. Rev. E, 104(5) (2021), 054114.

Evelyn Lamb, "Peculiar Pattern Found in 'Random' Prime Numbers", Nature, March 14, 2016, republished by Scientific American.

Robert J. Lemke Oliver and Kannan Soundararajan, Unexpected biases in the distribution of consecutive primes, arXiv preprint arXiv:1603.03720 [math.NT], 2016.

Index entries for sequences related to final digits of numbers.

Formula

a(n) = A010879(A000040(n)). - Michel Marcus, May 06 2014

Sum_k={1..n} a(k) ~ 5*n. - Amiram Eldar, Dec 11 2024

Maple

seq(ithprime(n) mod 10, n=1..105); # Nathaniel Johnston, Jun 29 2011

Mathematica

Table[Mod[Prime[n], 10], {n, 120}] (* Ray Chandler, Oct 01 2005 *)
Mod[Prime[Range[100]], 10] (* Vincenzo Librandi, May 06 2014 *)

Prog

(Magma) [Intseq(p)[1]: p in PrimesUpTo(600)]; // Bruno Berselli, Feb 14 2013
(Magma) [p mod 10: p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014
(PARI) a(n)=prime(n)%10 \\ Charles R Greathouse IV, Oct 13 2016
(PARI) primes(100)%10 \\ Charles R Greathouse IV, Oct 13 2016

Crossrefs

Cf. A000040, A010879, A110923, A039701-A039706, A038194, A039709-A039715, A290450.

Sequence in context: A073342 A074462 A113656 * A060418 A199975 A086355

Adjacent sequences: A007649 A007650 A007651 * A007653 A007654 A007655

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Simon Plouffe

Extensions

Extended by Ray Chandler, Oct 01 2005

Status

approved