A248701 Smallest prime such that the preceding n prime gaps are increasing and the following n prime gaps are decreasing.

3, 7, 359, 7853, 96401, 2812099, 294276293

Offset

1,1

Links

Table of n, a(n) for n=1..7.

Abhiram R Devesh, Python Code for Generating the Peak Primes

Example

a(3)=359; [347, 349, 353, 359, 367, 373, 379]; prime gaps [2, 4, 6, 8, 6, 6] which are monotonically increasing 2 <= 4 <= 6 and decreasing 8 >= 6 >=6.

Maple

A248701 := 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 17 2014

Prog

(PARI) isoka(i, n, vgp) = {for (k=0, n-2, if (vgp[i-k-1] > vgp[i-k], return(0)); if (vgp[i+k+1] < vgp[i+k+2], return(0)); ); return(1); }
a(n) = {nb = 10000; pa = prime(1); pb = prime(nb); vp = primes([pa, pb]); nbp = #vp; vgp = vector(nbp-1, k, vp[k+1] - vp[k]); ok = 0; while (!ok, for (i=1+n, nbp-n-1, if (isoka(i-1, n, vgp), ok = vp[i]; break); ); if (! ok, pa = prime(primepi(pb)-nb+n+1); pb = prime(primepi(pa)+nb); vp = primes([pa, pb]); nbp = #vp; vgp = vector(nbp-1, k, vp[k+1] - vp[k]); ); ); return (ok); } \\ Michel Marcus, Oct 17 2014

Crossrefs

Cf. A248702 - A248704.

Sequence in context: A064774 A348376 A089689 * A103317 A104051 A128004

Adjacent sequences: A248698 A248699 A248700 * A248702 A248703 A248704

Keyword

nonn,more

Author

Abhiram R Devesh, Oct 12 2014

Status

approved