A248704 - OEIS

%I #15 Dec 04 2014 15:11:58

%S 3,19,1429,25243,340577,1107791

%N Smallest prime such that the n preceding prime gaps are strictly decreasing and the n subsequent prime gaps strictly increasing.

%H Abhiram R Devesh, <a href="/A248704/a248704.py.txt">Python code for generating strict valley primes</a>

%e a(3)=1429 is in the middle of the sequence of successive primes [1409, 1423, 1427, 1429, 1433, 1439 , 1447] which have prime gaps [14, 4, 2, 4, 6, 8], and 14>4>2 is strictly decreasing and 4<6<8 is strictly increasing.

%p A248704 := proc(n)

%p     local glist,p,wrks,s ;

%p     if n = 0 then

%p         return ;

%p     else

%p         s := n+1 ;

%p         p := ithprime(s) ;

%p         glist := [seq(ithprime(i+1)-ithprime(i),i=1..2*n)] ;

%p         while true do

%p             wrks := true;

%p             for i from 1 to n-1 do

%p                 if glist[i] <= glist[i+1] then

%p                     wrks := false;

%p                     break;

%p                 end if;

%p             end do:

%p             if wrks then

%p                 for i from n+1 to 2*n-1 do

%p                     if glist[i] >= glist[i+1] then

%p                         wrks := false;

%p                         break;

%p                     end if;

%p                 end do:

%p             end if;

%p             if wrks then

%p                 return p;

%p             end if;

%p             p := nextprime(p) ;

%p             s := s+1 ;

%p             glist := subsop(1=NULL,glist) ;

%p             glist := [op(glist),ithprime(s+n)-ithprime(s+n-1)] ;

%p         end do:

%p     end if;

%p end proc: # _R. J. Mathar_, Dec 04 2014

%Y Cf. A248701, A248702, A248703.

%K nonn,more

%O 1,1

%A _Abhiram R Devesh_, Oct 12 2014