A248704 Smallest prime such that the n preceding prime gaps are strictly decreasing and the n subsequent prime gaps strictly increasing.

3, 19, 1429, 25243, 340577, 1107791

Offset

1,1

Links

Table of n, a(n) for n=1..6.

Abhiram R Devesh, Python code for generating strict valley primes

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

A248704 := proc(n)
    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 n-1 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*n-1 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+n-1)] ;
        end do:
    end if;
end proc: # R. J. Mathar, Dec 04 2014

Crossrefs

Cf. A248701, A248702, A248703.

Sequence in context: A258669 A192340 A326973 * A098796 A365579 A120563

Adjacent sequences: A248701 A248702 A248703 * A248705 A248706 A248707

Keyword

nonn,more

Author

Abhiram R Devesh, Oct 12 2014

Status

approved