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

1,2

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.

Links

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

Formula

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

Example

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.

Maple

Contribution from R. J. Mathar, Apr 24 2010: (Start)
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: (End)

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 *)

Crossrefs

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

Sequence in context: A008293 A185811 A011140 * A264605 A353245 A275928

Adjacent sequences: A171712 A171713 A171714 * A171716 A171717 A171718

Keyword

nonn

Author

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

Extensions

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

Status

approved