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A247248 a(n) = least k such that n divides 2^k + k. 1
1, 2, 1, 4, 4, 2, 6, 8, 7, 4, 3, 8, 12, 6, 7, 16, 16, 14, 18, 4, 19, 8, 22, 8, 33, 12, 7, 40, 11, 26, 23, 32, 8, 16, 6, 32, 5, 18, 37, 24, 40, 38, 42, 8, 7, 22, 10, 32, 61, 84, 38, 12, 35, 32, 46, 40, 32, 28, 24, 44, 17, 30, 61, 64, 66, 8, 66, 16, 67, 6, 11, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For every positive integer n, there exists an integer k such that 2^k + k is divisible by n. The proof is given in the link, p. 64.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

International Mathematical Olympiad, IMO-2006, p.64.

EXAMPLE

a(7)= 6 because 2^6+6 = 70 is divisible by 7.

MAPLE

f:= proc(n) local k;

for k from 1 do

  if 2^k + k mod n = 0 then return k fi

od

end proc:

seq(f(n), n=1..100); # Robert Israel, Dec 01 2014

MATHEMATICA

Table[s=0; k=0; While[k++; s=Mod[2^k+k, n]; s>0]; k, {n, 50}]

PROG

(Python)

def A247248(n):

....if n == 1:

........return 1

....else:

........x, k, kr = 1, 0, 0

........while (x+kr) % n:

............x, kr = (2*x) % n, (kr+1) % n

............k += 1

........return k

# Chai Wah Wu, Dec 03 2014

CROSSREFS

Cf. A135366, A006127 (2^n+n).

Sequence in context: A249140 A113421 A135366 * A192017 A180566 A051289

Adjacent sequences:  A247245 A247246 A247247 * A247249 A247250 A247251

KEYWORD

nonn

AUTHOR

Michel Lagneau, Dec 01 2014

STATUS

approved

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Last modified May 23 05:03 EDT 2019. Contains 323508 sequences. (Running on oeis4.)