A171715 Absolute value of (n-th prime of form 3*m-1 minus n-th prime of form 3*k+1/2+-1/2).

1, 2, 2, 2, 8, 8, 2, 14, 14, 14, 8, 14, 14, 8, 20, 26, 20, 20, 14, 14, 20, 20, 20, 26, 2, 8, 32, 26, 26, 44, 44, 50, 44, 38, 50, 26, 26, 38, 26, 32, 32, 20, 26, 20, 38, 38, 56, 62, 56, 68, 68, 80, 50, 50, 50, 44, 50, 62, 56, 50, 62, 74, 74, 62, 68, 56, 50, 44, 50, 50, 32, 44, 38

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 17 2009, Feb 09 02 2010

Keywords

• nonn

Comments

Also, the absolute value of (n-th generalized cuban prime minus n-th generalized non-cuban prime).

Or, the absolute value of n-th prime of form 6*m-3/2+-5/2 minus n-th prime of form 6*k-2+-1.

A003627 U A007645 = A045375 U A045410 = A000040.

Examples

			a(1) = abs(3*1-1-(3*1+1/2-1/2)) = 1; a(2) = abs(3*2-1-(3*2+1/2+1/2)) = 2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A003627, A007645, A045375, A045410.

Programs

Maple

A003627 := proc(n) if n <= 2 then op(n,[2,5]) ; ; else for a from procname(n-1)+2 by 2 do if isprime(a) and (a mod 3) =2 then return a ; end if; end do: end if; end proc:
A007645 := proc(n) if n <= 2 then op(n,[3,7]) ; ; else for a from procname(n-1)+2 by 2 do if isprime(a) and (a mod 3) <> 2 then return a ; end if; end do: end if; end proc:
A171715 := proc(n) abs(A003627(n)-A007645(n)) ; end proc: # R. J. Mathar, Apr 24 2010

Mathematica

Module[{nn=500,p1,p2,len},p1=Select[3*Range[nn]-1,PrimeQ];p2=Select[Flatten[#+{0,1}&/@ (3*Range[nn])],PrimeQ];len=Min[Length[p1],Length[p2]]; Abs[#[[1]]-#[[2]]]&/@ Thread[ {Take[p1,len],Take[p2,len]}]] (* Harvey P. Dale, Aug 29 2023 *)

Formula

a(n) = abs(A003627(n)-A007645(n)) = abs(A045375(n)-A045410(n)).

Extensions

Entries checked by R. J. Mathar, Apr 24 2010