cp's OEIS Frontend

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

%I A171715 #23 Jul 11 2025 16:06:45
%S A171715 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,
%T A171715 32,26,26,44,44,50,44,38,50,26,26,38,26,32,32,20,26,20,38,38,56,62,56,
%U A171715 68,68,80,50,50,50,44,50,62,56,50,62,74,74,62,68,56,50,44,50,50,32,44,38
%N A171715 Absolute value of (n-th prime of form 3*m-1 minus n-th prime of form 3*k+1/2+-1/2).
%C A171715 Also, the absolute value of (n-th generalized cuban prime minus n-th generalized non-cuban prime).
%C A171715 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.
%C A171715 A003627 U A007645 = A045375 U A045410 = A000040.
%H A171715 Harvey P. Dale, <a href="/A171715/b171715.txt">Table of n, a(n) for n = 1..1000</a>
%F A171715 a(n) = abs(A003627(n)-A007645(n)) = abs(A045375(n)-A045410(n)).
%e A171715 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.
%p A171715 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:
%p A171715 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:
%p A171715 A171715 := proc(n) abs(A003627(n)-A007645(n)) ; end proc: # _R. J. Mathar_, Apr 24 2010
%t A171715 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 *)
%Y A171715 Cf. A000040, A003627, A007645, A045375, A045410.
%K A171715 nonn
%O A171715 1,2
%A A171715 _Juri-Stepan Gerasimov_, Dec 17 2009, Feb 09 02 2010
%E A171715 Entries checked by _R. J. Mathar_, Apr 24 2010