OFFSET
1,4
COMMENTS
a(n) = 1 only if n is a prime.
a(2m) <= m, because with k=m, floor(2m/m)+(2m mod m) = 2.
a(2m+1) <= 2m: floor((2m+1)/2m) + ((2m+1) mod 2m) = 1 + 1 = 2.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
PROG
(Python)
primes = [2, 3]
primFlg = [0]*100000
primFlg[2] = primFlg[3] = 1
def appPrime(k):
for p in primes:
if k%p==0: return
if p*p > k: break
primes.append(k)
primFlg[k] = 1
for n in range(5, 100000, 6):
appPrime(n)
appPrime(n+2)
for n in range(1, 100000):
a = 0
for k in range(1, n):
c = n//k + n%k
if primFlg[c]: # if c in primes:
a = k
break
print(str(a), end=', ')
(Scheme)
;; MIT/GNU Scheme, with Aubrey Jaffer's SLIB Scheme library and function A234575bi as defined in A234575
(require 'factor) ;; For predicate prime? from SLIB-library.
(define (A234541 n) (let loop ((k 1)) (cond ((prime? (A234575bi n k)) k) ((> k n) 0) (else (loop (+ 1 k))))))
;; Antti Karttunen, Dec 29 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alex Ratushnyak, Dec 27 2013
STATUS
approved