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%I #18 Jun 05 2021 12:34:05
%S 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,
%T 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,
%U 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
%N Final digit of prime(n)*prime(n+1).
%C 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
%H Charles R Greathouse IV, <a href="/A137727/b137727.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A010879(A006094(n)). - _Felix Fröhlich_, Jun 05 2021
%t Table[ Mod[ Prime[n]*Prime[n+1], 10 ], {n,1,1000} ]
%t Mod[Times@@@Partition[Prime[Range[110]],2,1],10] (* _Harvey P. Dale_, Oct 05 2014 *)
%o (PARI) a(n)=prime(n)*prime(n+1)%10 \\ _Charles R Greathouse IV_, Dec 29 2012
%o (Python)
%o from sympy import prime
%o def a(n): return (prime(n)*prime(n+1))%10
%o print([a(n) for n in range(1, 106)]) # _Michael S. Branicky_, Jun 05 2021
%o (Python) # much faster alternate for initial segment of sequence
%o from sympy import nextprime
%o def aupton(terms):
%o p1, p2, alst = 2, 3, []
%o while len(alst) < terms:
%o p1, p2, alst = p2, nextprime(p2), alst + [(p1*p2)%10]
%o return alst
%o print(aupton(105)) # _Michael S. Branicky_, Jun 05 2021
%Y 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).
%K nonn,base
%O 1,1
%A _Alexander Adamchuk_, Feb 08 2008
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