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.

10, 19, 22, 30, 35, 40, 44, 48, 51, 59, 63, 66, 70, 73, 80, 87, 90, 93, 95, 102, 104, 106, 110, 115, 119, 122, 126, 132, 134, 138, 142, 147, 153, 156, 161, 165, 168, 171, 174, 176, 178, 184, 186, 193, 195, 198, 202, 204, 210, 216, 221, 224, 227, 230, 234, 236

Offset: 1

Author

Juri-Stepan Gerasimov, Feb 13 2010, Feb 15 2010

Keywords

• nonn

Comments

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

Examples

			a(1) = 6 + 4 = 10;
a(2) = 11 + 8 = 19;
a(3) = 13 + 9 = 22.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

GAP

A046953:=Filtered([1..250], k-> not IsPrime(6*k-1));;
A046954:=Filtered([0..250], n-> not IsPrime(6*n+1));;
Print(List([1..80], j->A046953[j]+A046954[j+1])); # G. C. Greubel, Feb 21 2019

Magma

A046953:=[n: n in [1..250] | not IsPrime(6*n-1)];
A046954:=[n: n in [0..250] | not IsPrime(6*n+1)];
[A046953[n] + A046954[n+1]: n in [1..80]]; // G. C. Greubel, Feb 21 2019

Maple

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:
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:
A173231 := proc(n) A046953(n)+A046954(n+1) ; end proc:
seq(A173231(n),n=1..120) ; # R. J. Mathar, May 02 2010

Mathematica

A046953:= Select[Range[250], !PrimeQ[6#-1] &];
A046954:= Select[Range[0, 250], !PrimeQ[6#+1] &];
Table[A046953[[n]] +A046954[[n+1]], {n,1,80}]

Sage

A046953=[n for n in (1..250) if not is_prime(6*n-1)];
A046954=[n for n in (0..250) if not is_prime(6*n+1)];
[A046953[n] + A046954[n+1] for n in (0..80)] # G. C. Greubel, Feb 21 2019

Formula

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

Extensions

Entries checked by R. J. Mathar, May 02 2010