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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
OFFSET
1,1
COMMENTS
See Tutaj (2014) for the precise definition.
LINKS
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.
Carl Pomerance, The Prime Number Graph, Mathematics of Computations, Volume 33, 145, January 1979, pages 399-408.
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
KEYWORD
nonn
AUTHOR
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