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A234541 Least k such that floor(n/k) + (n mod k) is a prime, or 0 if no such k exists. 1
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 (list; graph; refs; listen; history; text; internal format)
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 2)

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)+', ',

(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

Cf. A000040, A234575.

Sequence in context: A296131 A345344 A319004 * A066389 A077191 A317545

Adjacent sequences:  A234538 A234539 A234540 * A234542 A234543 A234544

KEYWORD

nonn,easy

AUTHOR

Alex Ratushnyak, Dec 27 2013

STATUS

approved

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Last modified December 3 22:32 EST 2021. Contains 349468 sequences. (Running on oeis4.)