A127818 a(n) is the least k such that the remainder when 10^k is divided by k is n.

3, 14, 7, 6, 35, 94, 993, 46, 22963573117, 11, 15084115509707, 22, 21, 86, 99985, 24, 221819, 82, 327, 1996, 28039, 26, 169, 38, 39, 74, 24257, 36, 10191082613, 65, 49, 34, 4739, 66, 99965, 188, 171, 62, 3753219157, 60, 3961, 58, 87, 76, 28315, 159, 10441

Offset: 1

Author

Alexander Adamchuk, Jan 30 2007

Keywords

• hard
• nonn

Comments

a(9) <= 22963573117 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 09 2007

a(11) <= 15084115509707 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 06 2007

a(29) <= 112237795073 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 09 2007

a(39) <= 3753219157 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 10 2007

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000 with -1 for large entries where a(n) has not yet been found

Crossrefs

Cf. A036236, A078457, A119678, A119679, A127816, A119715, A119714, A127817, A127819, A127820, A127821.

Programs

Mathematica

t = Table[0, {10000} ]; k = 1; While[ k < 4000000000, a = PowerMod[10, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t

Python

def a(n):
  k = 1
  while 10**k % k != n: k += 1
  return k
print([a(n) for n in range(1, 9)]) # Michael S. Branicky, Mar 14 2021

Extensions

Crump's values for a(9), a(11), a(39) confirmed, a(29) = 10191082613 = 16763 * 607951 by Hagen von Eitzen, Jul 29 2009