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%I #24 Oct 13 2023 10:02:07
%S 1,3,5,9,129,1179,21105,96525,419925,13690959,8403613179
%N Beginning with 1, a(i)*a(j) + 2 is prime for all i, j, i != j.
%C All terms are odd and equal to p - 2 for some prime p. Definition assumes that a(i+1) > a(i) as otherwise adding 1 to any initial subsequence would still satisfy the definition. - _Chai Wah Wu_, Jan 12 2019
%C For n >= 2, the last digit of a(n) is 5 or 9. - _Pontus von Brömssen_, Oct 12 2023
%e 1*3 + 2, 3*5 + 2, 1*5 + 2, etc. are primes.
%e 9*1 + 2 = 11, 9*3 + 2 = 29, 9*5 + 2 = 47 are all primes, therefore a(4) = 9.
%t a = {1}; For[n = 2, n < 1000000, n++, b = Table[a[[i]]*n + 2, {i, 1, Length[ a]}]; If[Union[PrimeQ[b], PrimeQ[b]] == {True}, AppendTo[a, n]]]; a (* _Stefan Steinerberger_, Jun 02 2007 *)
%Y Cf. A083518.
%K hard,more,nonn
%O 0,2
%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 05 2003
%E Corrected and extended by _Stefan Steinerberger_, Jun 02 2007
%E a(10) from _Donovan Johnson_, Nov 11 2008
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