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%I #21 Mar 23 2024 05:04:04
%S 180179,270269,300299,330329,390389,420419,540539,660659,840839,
%T 1231229,1261259,1501499,1621619,1861859,1921919,1951949,2012009,
%U 2372369,2762759,2972969,3663659,3693689,3723719,3903899,4084079
%N Smaller of twin primes whose mean (average) is a multiple of A002110(6)=30030.
%H Robert Israel, <a href="/A060232/b060232.txt">Table of n, a(n) for n = 1..10000</a> (first 642 terms from Muniru A Asiru)
%e For the pair {5735729,5735731} (5735729+5735731)/2 = 191*30030.
%p for n from 1 to 10^5 do if (ithprime(n+1) - ithprime(n)) = 2 and (ithprime(n+1) + ithprime(n)) mod 30030 = 0 then print(ithprime(n)); fi; od; # _Muniru A Asiru_, Jan 29 2018
%p # More efficient:
%p select(t -> isprime(t) and isprime(t+2), [seq(30030*k-1, k=1..10^3)]); # _Robert Israel_, Jan 29 2018
%t Select[Partition[Prime[Range[300000]],2,1],#[[2]]-#[[1]]==2&&Divisible[Mean[ #],30030]&][[All,1]] (* _Harvey P. Dale_, Apr 23 2022 *)
%o (GAP) P:=Filtered([1..10^5], IsPrime);;
%o P1:=List(Filtered(Filtered(List([1..Length(P)-1], n -> [P[n],P[n+1]]),i -> i[2]-i[1]=2), j -> (j[1] + j[2]) mod 30030 = 0), k -> k[1]); # _Muniru A Asiru_, Jan 29 2018
%Y Cf. A001359, A002110, A060229, A060230, A060231.
%K nonn
%O 1,1
%A _Labos Elemer_, Mar 21 2001
%E Minor edits by _Ray Chandler_, Apr 04 2009
%E Definition clarified by _Harvey P. Dale_, Apr 23 2022
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