login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A319126 Convex hull primes, that is, prime numbers corresponding to the convex hull of PrimePi, the prime counting function. 0
2, 3, 5, 7, 13, 19, 23, 31, 43, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

"Convex hull of PrimePi" is a short wording for "the upper convex hull of the points {p, PrimePi(p)} for p >= 2".

LINKS

Table of n, a(n) for n=1..42.

Wikipedia, Convex hull

EXAMPLE

Prime 83 is not member because there exist two primes from the convex hull, namely 47 and 113, such that (PrimePi(83) - PrimePi(47))/(83 - 47) < (PrimePi(113) - PrimePi(83))/(113 - 83).

MATHEMATICA

terms = 42;

pMax = 110000;

a[1] = 2;

a[n_] := a[n] = Module[{}, For[slopeMax = 0; p1 = NextPrime[a[n-1]], p1 <= pMax, p1 = NextPrime[p1], slope = (PrimePi[p1] - PrimePi[a[n-1]])/(p1 - a[n-1]); If[slope > slopeMax, slopeMax = slope; p1Max = p1]]; p1Max];

Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 42}]

CROSSREFS

Cf. A000720, A124661, A167844, A246033 (a subsequence).

Sequence in context: A153591 A038917 A124661 * A134266 A233043 A231099

Adjacent sequences:  A319123 A319124 A319125 * A319127 A319128 A319129

KEYWORD

nonn,more

AUTHOR

Jean-Fran├žois Alcover, Sep 11 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 23:45 EDT 2020. Contains 334581 sequences. (Running on oeis4.)