%I #24 Aug 14 2024 08:37:15
%S 4,7,13,23,37,53,67,97,103,131,139,173,181,193,223,233,263,277,307,
%T 337,409,421,457,509,563,593,613,631,653,797,811,823,853,877,1013,
%U 1021,1039,1051,1087,1129,1223,1259,1283,1297,1307,1423,1447,1471,1483,1601
%N k between A001359(n) and A001359(n+1) such that A073830(k) is maximal.
%C A073830(a(n)) = A073831(n).
%H Michael S. Branicky, <a href="/A073832/b073832.txt">Table of n, a(n) for n = 1..2600</a>
%p A073832 := proc(n)
%p local k,kmx,a ;
%p kmx := 0 ;
%p a := A001359(n)+1 ;
%p for k from A001359(n)+1 to A001359(n+1)-1 do
%p if A073830(k) > kmx then
%p a := k ;
%p kmx := A073830(k) ;
%p end if;
%p end do:
%p a ;
%p end proc:
%p seq(A073832(n),n=1..50) ; # _R. J. Mathar_, Feb 21 2017
%t f[n_] := Mod[4*((n - 1)! + 1) + n, n*(n + 2)];
%t pp = Select[Prime[Range[300]], PrimeQ[# + 2] & ];
%t a[n_] := MaximalBy[Range[pp[[n]], pp[[n + 1]]], f];
%t Array[a, Length[pp] - 1] // Flatten (* _Jean-François Alcover_, Feb 22 2018 *)
%o (Python)
%o from math import factorial
%o from itertools import islice, pairwise
%o from sympy import isprime, nextprime, primerange
%o def f(n): return (4*(factorial(n-1) + 1) + n)%(n*(n + 2))
%o def bgen(): # generator of A001359
%o p, q = 2, 3
%o while True:
%o if q - p == 2: yield p
%o p, q = q, nextprime(q)
%o def agen(): # generator of terms
%o for p, q in pairwise(bgen()):
%o yield max((f(k), k) for k in range(p+1, q))[1]
%o print(list(islice(agen(), 80))) # _Michael S. Branicky_, Aug 13 2024
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Aug 12 2002