

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
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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[n1]], p1 <= pMax, p1 = NextPrime[p1], slope = (PrimePi[p1]  PrimePi[a[n1]])/(p1  a[n1]); 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

JeanFrançois Alcover, Sep 11 2018


STATUS

approved



