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A234541
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Least k such that floor(n/k) + (n mod k) is a prime, or 0 if no such k exists.
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1
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0, 1, 1, 2, 1, 2, 1, 4, 2, 2, 1, 4, 1, 2, 3, 8, 1, 6, 1, 4, 2, 2, 1, 8, 2, 2, 5, 4, 1, 6, 1, 6, 2, 2, 3, 12, 1, 2, 3, 8, 1, 6, 1, 4, 2, 2, 1, 16, 3, 10, 3, 4, 1, 18, 3, 6, 2, 2, 1, 8, 1, 2, 6, 18, 3, 6, 1, 4, 3, 4, 1, 14, 1, 2, 9, 4, 5, 6, 1, 16, 2, 2, 1, 12, 2, 2
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OFFSET
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1,4
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COMMENTS
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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.
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LINKS
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PROG
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(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))))))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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