A054690 - OEIS

%I #8 Jul 29 2018 13:56:42

%S 7,19,43,73,73,349,349,349,349,349,349,661,661,661,661,661,661,661,

%T 661,8629,8629,8629,8629,13399,13399,13399,14629,14629,24421,24421,

%U 24421,24421,24421,24421,24421,24421,24421,24421,24421,24421,24421

%N n consecutive primes differ by 4 or more starting at a(n), or n consecutive primes with no twin primes.

%H Robert Israel, <a href="/A054690/b054690.txt">Table of n, a(n) for n = 2..204</a>

%p P:= select(isprime, [seq(i,i=3..10^7,2)]):

%p A:= 'A':

%p state:= 0: smax := 0:

%p for i from 2 to nops(P) do

%p   if P[i] - P[i-1] >= 4 then

%p     state:= state + 1;

%p     if state > smax then smax:= state; A[state+1]:= P[i-state] fi

%p   else

%p     state:= 0;

%p   fi

%p od:

%p seq(A[i],i=2..smax+1); # _Robert Israel_, Jun 27 2017

%t Prime[#]&/@With[{pd=If[#>2,1,0]&/@Differences[Prime[Range[3000]]]}, Flatten[ Table[ SequencePosition[pd,PadRight[{},n,1],1][[All,1]],{n,45}]]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 29 2018 *)

%Y Cf. A054691, A054692.

%K nonn

%O 2,1

%A _Jeff Burch_, Apr 19 2000