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

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