A073832 k between A001359(n) and A001359(n+1) such that A073830(k) is maximal.

4, 7, 13, 23, 37, 53, 67, 97, 103, 131, 139, 173, 181, 193, 223, 233, 263, 277, 307, 337, 409, 421, 457, 509, 563, 593, 613, 631, 653, 797, 811, 823, 853, 877, 1013, 1021, 1039, 1051, 1087, 1129, 1223, 1259, 1283, 1297, 1307, 1423, 1447, 1471, 1483, 1601

Offset: 1

Author

Reinhard Zumkeller, Aug 12 2002

Keywords

• nonn

Comments

A073830(a(n)) = A073831(n).

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..2600

Programs

Maple

A073832 := proc(n)
    local k,kmx,a ;
    kmx := 0 ;
    a := A001359(n)+1 ;
    for k from A001359(n)+1 to A001359(n+1)-1 do
        if A073830(k) > kmx then
            a := k ;
            kmx := A073830(k) ;
        end if;
    end do:
    a ;
end proc:
seq(A073832(n),n=1..50) ; # R. J. Mathar, Feb 21 2017

Mathematica

f[n_] := Mod[4*((n - 1)! + 1) + n, n*(n + 2)];
pp = Select[Prime[Range[300]], PrimeQ[# + 2] & ];
a[n_] := MaximalBy[Range[pp[[n]], pp[[n + 1]]], f];
Array[a, Length[pp] - 1] // Flatten (* Jean-François Alcover, Feb 22 2018 *)

Python

from math import factorial
from itertools import islice, pairwise
from sympy import isprime, nextprime, primerange
def f(n): return (4*(factorial(n-1) + 1) + n)%(n*(n + 2))
def bgen(): # generator of A001359
    p, q = 2, 3
    while True:
        if q - p == 2: yield p
        p, q = q, nextprime(q)
def agen(): # generator of terms
    for p, q in pairwise(bgen()):
        yield max((f(k), k) for k in range(p+1, q))[1]
print(list(islice(agen(), 80))) # Michael S. Branicky, Aug 13 2024