A110923 -id:A110923 - cp's OEIS frontend

A007652 Final digit of prime(n).

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

N. J. A. Sloane, Simon Plouffe

Primes modulo 10.

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).

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.

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

[Intseq(p)[1]: p in PrimesUpTo(600)]; // Bruno Berselli, Feb 14 2013

[p mod 10: p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014

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

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

a(n)=prime(n)%10 \\ Charles R Greathouse IV, Oct 13 2016

primes(100)%10 \\ Charles R Greathouse IV, Oct 13 2016

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

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

Extended by Ray Chandler, Oct 01 2005

A242119 Primes modulo 18.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 1, 5, 11, 13, 1, 5, 7, 11, 17, 5, 7, 13, 17, 1, 7, 11, 17, 7, 11, 13, 17, 1, 5, 1, 5, 11, 13, 5, 7, 13, 1, 5, 11, 17, 1, 11, 13, 17, 1, 13, 7, 11, 13, 17, 5, 7, 17, 5, 11, 17, 1, 7, 11, 13, 5, 1, 5, 7, 11, 7, 13, 5, 7, 11, 17, 7, 13, 1, 5

Offset: 1

Vincenzo Librandi, May 05 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. sequences of the type Primes mod k: A039701 (k=3), A039702 (k=4), A039703 (k=5), A039704 (k=6), A039705 (k=7), A039706 (k=8), A038194 (k=9), A007652 (k=10), A039709 (k=11), A039710 (k=12), A039711 (k=13), A039712 (k=14), A039713 (k=15), A039714 (k=16), A039715 (k=17), this sequence (k=18), A033633 (k=19), A242120(k=20), A242121 (k=21), A242122 (k=22), A229786 (k=23), A229787 (k=24), A242123 (k=25), A242124 (k=26), A242125 (k=27), A242126 (k=28), A242127 (k=29), A095959 (k=30), A110923 (k=100).

Magma
```
[p mod(18): p in PrimesUpTo(500)];
```
Mathematica
```
Mod[Prime[Range[100]], 18]
```

[mod(p, 18) for p in primes(500)] # Bruno Berselli, May 05 2014

Sum_{i=1..n} a(i) ~ 9n. The derivation is the same as in the formula in A039715. - Jerzy R Borysowicz, Apr 27 2022

A137727 Final digit of prime(n)*prime(n+1).

Original entry on oeis.org

6, 5, 5, 7, 3, 1, 3, 7, 7, 9, 7, 7, 3, 1, 1, 7, 9, 7, 7, 3, 7, 7, 7, 3, 7, 3, 1, 3, 7, 1, 7, 7, 3, 1, 9, 7, 1, 1, 1, 7, 9, 1, 3, 1, 3, 9, 3, 1, 3, 7, 7, 9, 1, 7, 1, 7, 9, 7, 7, 3, 9, 1, 7, 3, 1, 7, 7, 9, 3, 7, 7, 3, 1, 7, 7, 7, 3, 7, 9, 1, 9, 1, 3, 7, 7, 7, 3, 7, 3, 1, 3, 3, 7, 9, 7, 7, 9, 3, 3, 7, 9, 1, 7, 9, 7

Offset: 1

Alexander Adamchuk, Feb 08 2008

a(n) is 1, 3, 7, or 9 for n > 3. I conjecture that 1 and 9 appear 17/66 of the time and 3 and 7 appear 8/33 of the time. - Charles R Greathouse IV, Jan 03 2013

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A006094 (Products of 2 successive primes), A007652 (Final digit of prime(n)), A010879 (final digit of n), A110923 (final two digits of prime(n) (with leading zero omitted)), A137728 (second digit from the end of product of first n primes).

Table[ Mod[ Prime[n]*Prime[n+1], 10 ], {n,1,1000} ]
Mod[Times@@@Partition[Prime[Range[110]],2,1],10] (* Harvey P. Dale, Oct 05 2014 *)

a(n)=prime(n)*prime(n+1)%10 \\ Charles R Greathouse IV, Dec 29 2012

from sympy import prime
def a(n): return (prime(n)*prime(n+1))%10
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Jun 05 2021

# much faster alternate for initial segment of sequence
from sympy import nextprime
def aupton(terms):
    p1, p2, alst = 2, 3, []
    while len(alst) < terms:
        p1, p2, alst = p2, nextprime(p2), alst + [(p1*p2)%10]
    return alst
print(aupton(105)) # Michael S. Branicky, Jun 05 2021

a(n) = A010879(A006094(n)). - Felix Fröhlich, Jun 05 2021

A137728 Second digit from the end of product of first n primes.

Original entry on oeis.org

0, 0, 3, 1, 1, 3, 1, 9, 7, 3, 3, 1, 1, 3, 1, 3, 7, 7, 9, 9, 7, 3, 9, 1, 7, 7, 1, 7, 3, 9, 3, 3, 1, 9, 1, 1, 7, 1, 7, 1, 9, 9, 9, 7, 9, 1, 1, 3, 1, 9, 7, 3, 3, 3, 1, 3, 7, 7, 9, 9, 7, 1, 7, 7, 1, 7, 7, 9, 3, 7, 1, 9, 3, 9, 1, 3, 7, 9, 9, 1, 9, 9, 9, 7, 3, 9, 1, 7, 7, 1, 7, 3, 1, 1, 9, 7, 3, 3, 9, 9, 3, 1, 3, 7, 7

Offset: 1

Alexander Adamchuk, Feb 08 2008

a(1) = a(2) = 0 because prime(1) = 2 and prime(1)*prime(2) = 6 are one-digit numbers.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007652 = Final digit of prime(n).
Cf. A110923 = Final two digits of prime(n).
Cf. A137727 = Final digit of prime(n)*prime(n+1).
Cf. A002110 = Primorial numbers, p#.

a[1]:= 0: a[2]:= 0: a[3]:= 3: p:= 5:
for n from 4 to 1000 do
  p:= nextprime(p);
  a[n]:= (a[n-1] * p) mod 10:
od: # Robert Israel, Nov 22 2018

a(1) = a(2) = 0, for n>2 Table[ Mod[ Product[ Prime[n], {n,1,k} ], 100 ]/10, {k,3,1000} ]

a(n) = A002110(n)/10 mod 10 for n > 2; a(1) = a(2) = 0.

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A007652 Final digit of prime(n).

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A242119 Primes modulo 18.

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A137727 Final digit of prime(n)*prime(n+1).

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A137728 Second digit from the end of product of first n primes.

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