A248702 Smallest prime such that the n preceding prime gaps are monotonically decreasing and the n following prime gaps are monotonically increasing.

2, 3, 19, 43, 2687, 179819, 1107791

Offset

0,1

Comments

a(7) >= 8960453, if it exists. - R. J. Mathar, Dec 04 2014

Links

Table of n, a(n) for n=0..6.

Abhiram R Devesh, Python code for generating the valley primes

Example

a(n=3) = 43 because it is in the middle of the consecutive primes [31 , 37 , 41 , 43 , 47 , 53 , 59] which define the sequence of 2n=6 prime gaps [6, 4, 2, 4, 6, 6], where 6>=4>=2 is monotonically decreasing and 4<=6<=6 is monotonically increasing.

Maple

A248702 := 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:
            for i from n+1 to 2*n-1 do
                if glist[i] > glist[i+1] then
                    wrks := false;
                    break;
                end if;
            end do:
            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. A001223, A248701, A248703, A248704.

Sequence in context: A051079 A051089 A289860 * A171149 A157042 A128968

Adjacent sequences: A248699 A248700 A248701 * A248703 A248704 A248705

Keyword

nonn,more

Author

Abhiram R Devesh, Oct 12 2014

Status

approved