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A173231 a(n) is the n-th number m such that 6*m-1 is composite plus the n-th number k such that 6*k+1 is composite.

%I A173231 #19 Sep 08 2022 08:45:50
%S A173231 10,19,22,30,35,40,44,48,51,59,63,66,70,73,80,87,90,93,95,102,104,106,
%T A173231 110,115,119,122,126,132,134,138,142,147,153,156,161,165,168,171,174,
%U A173231 176,178,184,186,193,195,198,202,204,210,216,221,224,227,230,234,236
%N A173231 a(n) is the n-th number m such that 6*m-1 is composite plus the n-th number k such that 6*k+1 is composite.
%C A173231 A001477 = A002822 U A171696 U A067611 where A067611 = A121763 U A121765; A121763 = A046954 U A171696 and A121765 = A046953 U A171696.
%H A173231 G. C. Greubel, <a href="/A173231/b173231.txt">Table of n, a(n) for n = 1..10000</a>
%F A173231 a(n) = A046953(n) + A046954(n+1).
%e A173231 a(1) = 6 + 4 = 10;
%e A173231 a(2) = 11 + 8 = 19;
%e A173231 a(3) = 13 + 9 = 22.
%p A173231 A046953 := proc(n) if n = 1 then 6 ; else for a from procname(n-1)+1 do if not isprime(6*a-1) then return a; end if; end do: end if; end proc:
%p A173231 A046954 := proc(n) if n = 1 then 0 ; else for a from procname(n-1)+1 do if not isprime(6*a+1) then return a; end if; end do: end if; end proc:
%p A173231 A173231 := proc(n) A046953(n)+A046954(n+1) ; end proc:
%p A173231 seq(A173231(n),n=1..120) ; # _R. J. Mathar_, May 02 2010
%t A173231 A046953:= Select[Range[250], !PrimeQ[6#-1] &];
%t A173231 A046954:= Select[Range[0, 250], !PrimeQ[6#+1] &];
%t A173231 Table[A046953[[n]] +A046954[[n+1]], {n,1,80}]
%o A173231 (Magma)
%o A173231 A046953:=[n: n in [1..250] | not IsPrime(6*n-1)];
%o A173231 A046954:=[n: n in [0..250] | not IsPrime(6*n+1)];
%o A173231 [A046953[n] + A046954[n+1]: n in [1..80]]; // _G. C. Greubel_, Feb 21 2019
%o A173231 (Sage)
%o A173231 A046953=[n for n in (1..250) if not is_prime(6*n-1)];
%o A173231 A046954=[n for n in (0..250) if not is_prime(6*n+1)];
%o A173231 [A046953[n] + A046954[n+1] for n in (0..80)] # _G. C. Greubel_, Feb 21 2019
%o A173231 (GAP)
%o A173231 A046953:=Filtered([1..250], k-> not IsPrime(6*k-1));;
%o A173231 A046954:=Filtered([0..250], n-> not IsPrime(6*n+1));;
%o A173231 Print(List([1..80], j->A046953[j]+A046954[j+1])); # _G. C. Greubel_, Feb 21 2019
%Y A173231 Cf. A001477, A002822, A067611, A046953, A046954, A121763, A121765, A171696.
%K A173231 nonn
%O A173231 1,1
%A A173231 _Juri-Stepan Gerasimov_, Feb 13 2010, Feb 15 2010
%E A173231 Entries checked by _R. J. Mathar_, May 02 2010