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A246033 "Convex" primes: extremal primes in the sense of Tutaj. 4
2, 3, 7, 19, 47, 73, 113, 199, 283, 467, 661, 887, 1129, 1327, 1627, 2803, 3947, 4297, 5881, 6379, 7043, 9949, 10343, 13187, 15823, 18461, 24137, 33647, 34763, 37663, 42863, 43067, 59753, 59797, 82619, 96017, 102679, 129643, 130699, 142237, 155893, 187477, 194119 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See Tutaj (2014) for the precise definition.

REFERENCES

Pommerance, Carl.: The Prime Number Graph, Mathematics of Computations, Volume 33, 145, January 1979, pages 399-408.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..500

Nathan McNew, The Most Frequent Values of the Largest Prime Divisor Function, Exper. Math., 2017, Vol. 26, No. 2, 210-224; also arXiv:1504.05985 [math.NT], 2015.

Edward Tutaj, Prime numbers with a certain extremal type property, arXiv:1408.3609 [math.NT], 2014.

MAPLE

plist := [2, 3] ;

nlist := [1, 2] ;

p := 5 ;

for n from 3 to 100000 do # experimental upper limit!

    plist := [op(plist), p] ;

    nlist := [op(nlist), n] ;

    doflat := true ;

    while doflat do

        doflat := false ;

        for nrew from nops(nlist)-1 to 2 by -1 do

            slopold := (nlist[nrew]-nlist[nrew-1])/(plist[nrew]-plist[nrew-1]) ;

            slop := (nlist[nrew+1]-nlist[nrew])/(plist[nrew+1]-plist[nrew]) ;

            if slop >= slopold then

                plist := subsop(nrew=NULL, plist) ;

                nlist := subsop(nrew=NULL, nlist) ;

                doflat := true ;

            end if;

        end do:

    end do:

    print(plist) ;

    p := nextprime(p) ;

end do: # R. J. Mathar, Jul 28 2017

MATHEMATICA

terms = 50; nmax0 = 25000; dnmax = 1000; Clear[f];

f[nmax_] := f[nmax] = Module[{}, plist = {2, 3}; nlist = {1, 2}; p = 5;

For[n = 3, n <= nmax, n++,

plist = Append[plist, p];

nlist = Append[nlist, n]; doflat = True;

While[doflat, doflat = False;

For[nrew = Length[nlist]-1, nrew >= 2, nrew--, slopold = (nlist[[nrew]] - nlist[[nrew-1]])/(plist[[nrew]] - plist[[nrew-1]]); slop = (nlist[[nrew+1]] - nlist[[nrew]])/(plist[[nrew+1]] - plist[[nrew]]); If [slop >= slopold, plist [[nrew]] = Nothing nlist[[nrew]] = Nothing; doflat = True]]

]; p = NextPrime[p]

]; PadRight[plist, terms]

];

f[nmax = nmax0]; f[nmax = nmax + dnmax];

While[Print[nmax]; f[nmax][[1 ;; terms]] != f[nmax - dnmax][[1 ;; terms]], nmax = nmax + dnmax];

f[nmax] (* Jean-François Alcover, Nov 01 2018, from R. J. Mathar's Maple code *)

CROSSREFS

A different notion of convex prime is mentioned in A167844.

Sequence in context: A091410 A069051 A229290 * A122724 A256758 A033844

Adjacent sequences:  A246030 A246031 A246032 * A246034 A246035 A246036

KEYWORD

nonn

AUTHOR

Michel Marcus and N. J. A. Sloane, Aug 18 2014

EXTENSIONS

a(14) corrected by Edward Tutaj and Charles R Greathouse IV, Nov 27 2014

Primes beyond 33647 from R. J. Mathar, Jul 28 2017

STATUS

approved

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Last modified November 17 11:02 EST 2019. Contains 329226 sequences. (Running on oeis4.)