A073832 - OEIS

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

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OFFSET

1,1

COMMENTS

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

LINKS

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

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 *)

PROG

(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

CROSSREFS

Sequence in context: A298354 A139217 A038391 * A265160 A090854 A039694

Adjacent sequences: A073829 A073830 A073831 * A073833 A073834 A073835

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 12 2002

STATUS

approved