A173231 - OEIS

%I #19 Sep 08 2022 08:45:50

%S 10,19,22,30,35,40,44,48,51,59,63,66,70,73,80,87,90,93,95,102,104,106,

%T 110,115,119,122,126,132,134,138,142,147,153,156,161,165,168,171,174,

%U 176,178,184,186,193,195,198,202,204,210,216,221,224,227,230,234,236

%N 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 A001477 = A002822 U A171696 U A067611 where A067611 = A121763 U A121765; A121763 = A046954 U A171696 and A121765 = A046953 U A171696.

%H G. C. Greubel, <a href="/A173231/b173231.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A046953(n) + A046954(n+1).

%e a(1) = 6 + 4 = 10;

%e a(2) = 11 + 8 = 19;

%e a(3) = 13 + 9 = 22.

%p 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 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 := proc(n) A046953(n)+A046954(n+1) ; end proc:

%p seq(A173231(n),n=1..120) ; # _R. J. Mathar_, May 02 2010

%t A046953:= Select[Range[250], !PrimeQ[6#-1] &];

%t A046954:= Select[Range[0, 250], !PrimeQ[6#+1] &];

%t Table[A046953[[n]] +A046954[[n+1]], {n,1,80}]

%o (Magma)

%o A046953:=[n: n in [1..250] | not IsPrime(6*n-1)];

%o A046954:=[n: n in [0..250] | not IsPrime(6*n+1)];

%o [A046953[n] + A046954[n+1]: n in [1..80]]; // _G. C. Greubel_, Feb 21 2019

%o (Sage)

%o A046953=[n for n in (1..250) if not is_prime(6*n-1)];

%o A046954=[n for n in (0..250) if not is_prime(6*n+1)];

%o [A046953[n] + A046954[n+1] for n in (0..80)] # _G. C. Greubel_, Feb 21 2019

%o (GAP)

%o A046953:=Filtered([1..250], k-> not IsPrime(6*k-1));;

%o A046954:=Filtered([0..250], n-> not IsPrime(6*n+1));;

%o Print(List([1..80], j->A046953[j]+A046954[j+1])); # _G. C. Greubel_, Feb 21 2019

%Y Cf. A001477, A002822, A067611, A046953, A046954, A121763, A121765, A171696.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Feb 13 2010, Feb 15 2010

%E Entries checked by _R. J. Mathar_, May 02 2010