A092188 a(n) = smallest positive integer m such that 2^3^4^5^...^n == m (mod n).

2, 2, 4, 2, 2, 1, 8, 8, 2, 2, 8, 5, 8, 2, 16, 2, 8, 18, 12, 8, 2, 16, 8, 2, 18, 26, 8, 11, 2, 2, 32, 2, 2, 22, 8, 31, 18, 5, 32, 2, 8, 27, 24, 17, 16, 8, 32, 43, 2, 2, 44, 45, 26, 2, 8, 56, 40, 47, 32, 33, 2, 8, 64, 57, 2, 5, 36, 62, 22, 60, 8, 1, 68, 2, 56, 57, 44, 8, 32, 80, 2, 2, 8, 2, 70

Offset

2,1

Links

Max Alekseyev, Table of n, a(n) for n = 2..1000

R. Munafo, Smallest positive integer m such that 2^3^4^5^...^n == m mod n

Formula

a(n) = n if n is a power of 2; otherwise a(n) = (2^3^4^5^...^n) mod n = A213013(n). [From Max Alekseyev, Jun 02 2012]

Example

2^3^4^5 = 2^3^1024. But 3 == -1 (mod 4), so 3^1024 == 1 (mod 4), so 2^3^1024 == 2^1 (mod 5) since 2^4 == 1 (mod 5). Thus a(5) = 2.

Crossrefs

Sequence in context: A021450 A239675 A289827 * A340675 A372905 A356497

Adjacent sequences: A092185 A092186 A092187 * A092189 A092190 A092191

Keyword

nonn,nice

Author

N. J. A. Sloane, following a suggestion of J. H. Conway, Apr 02 2004

Extensions

More terms from Robert Munafo, Apr 11 2004

Status

approved