

A248704


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


4




OFFSET

1,1


LINKS



EXAMPLE

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.


MAPLE

local glist, p, wrks, s ;
if n = 0 then
return ;
else
s := n+1 ;
p := ithprime(s) ;
glist := [seq(ithprime(i+1)ithprime(i), i=1..2*n)] ;
while true do
wrks := true;
for i from 1 to n1 do
if glist[i] <= glist[i+1] then
wrks := false;
break;
end if;
end do:
if wrks then
for i from n+1 to 2*n1 do
if glist[i] >= glist[i+1] then
wrks := false;
break;
end if;
end do:
end if;
if wrks then
return p;
end if;
p := nextprime(p) ;
s := s+1 ;
glist := subsop(1=NULL, glist) ;
glist := [op(glist), ithprime(s+n)ithprime(s+n1)] ;
end do:
end if;


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



