A119678 a(n) is the least k such that 4^k mod k = n.

3, 14, 137243, 5, 6821, 10, 57, 124, 35, 18, 2791496231, 244, 51, 505, 199534799, 20, 30271293169, 49, 45, 236, 399531841, 42, 533, 25, 39, 50, 352957, 36, 995, 98, 33, 112, 47503, 55, 42345881, 44, 2981, 289, 805, 78, 1019971289, 25498, 2121, 212

Offset: 1

Author

Ryan Propper, Jun 12 2006

Keywords

• nonn

Comments

a(n) > n.

Numbers n > 1 such that a(n-1) = n are listed in A015950.

a(87) > 10^14.

a(11) <= 2791496231, a(17) <= 140631956671, a(53) <= 52134328061 from Joe K. Crump (joecr(AT)carolina.rr.com), Feb 10 2007

Links

• Ryan Propper, Table of n, a(n) for n = 1..82
• Robert G. Wilson v, Table of n, a(n) for n = 1..10000 with -1 for those entries where a(n) has not yet been found

Crossrefs

Cf. A015950, A036236, A078457, A119679, A127816, A119715, A119714, A127817, A127818, A127819, A127820, A127821.

Programs

Mathematica

Do[k = 1; While[PowerMod[4, k, k] != n, k++ ]; Print[k], {n, 30}]
t = Table[0, {10000} ]; k = 1; While[ k < 5000000000, a = PowerMod[4, k, k]; If[a < 10001 && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++ ]; t (* search limits expanded by Robert G. Wilson v, Jul 14 2009 *)

Python

def a(n):
  k = 1
  while 4**k % k != n: k += 1
  return k
print([a(n) for n in range(1, 11)]) # Michael S. Branicky, Mar 14 2021

Formula

a(5^k-1) = 5^k.

Extensions

a(11) = 2791496231 from Robert G. Wilson v, Feb 11 2007; confirmed by Ryan Propper, Feb 15 2007

Link corrected by R. J. Mathar, Jul 24 2009

a(83) = 3085807457009 = 113 * 331 * 82501603 from Hagen von Eitzen, Jul 27 2009