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

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

1,1

Comments

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

Links

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

Formula

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

Mathematica

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 *)

Prog

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

Crossrefs

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).

Sequence in context: A381473 A021608 A108088 * A010497 A167918 A070860

Adjacent sequences: A137724 A137725 A137726 * A137728 A137729 A137730

Keyword

nonn,base

Author

Alexander Adamchuk, Feb 08 2008

Status

approved