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k between A001359(n) and A001359(n+1) such that A073830(k) is maximal.
3

%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