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%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
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