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

Author

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

Keywords

• nonn
• nice

Examples

			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.
		

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]

Extensions

More terms from Robert Munafo, Apr 11 2004