A373495 a(1) = 2; thereafter, a(n) = prime(n)^prime(n-1) (mod 10).

2, 9, 5, 7, 1, 7, 7, 9, 7, 9, 1, 3, 1, 3, 3, 7, 9, 1, 7, 1, 7, 9, 7, 9, 7, 1, 3, 3, 9, 3, 7, 1, 3, 9, 9, 1, 3, 3, 3, 7, 9, 1, 1, 7, 7, 9, 1, 7, 3, 9, 3, 9, 1, 1, 3, 3, 9, 1, 3, 1, 3, 7, 7, 1, 7, 7, 1, 3, 7, 9, 3, 9, 3, 7, 9, 7, 9, 7, 1, 9, 9, 1, 1, 7, 9, 7, 9, 7, 1, 3, 3, 9, 3, 1, 9, 7, 9, 1, 3, 1, 7, 3, 3, 9, 1

Offset: 1

Author

Robert G. Wilson v, Jun 06 2024

Keywords

• nonn

Comments

This sequence is not periodic.

Examples

			a(2) = 3^2 (mod 10) = 9.
a(3) = 5^3 (mod 10) = 5.
		

References

• Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing, Redwood City, CA, 1991, p. 226-229.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Robert P. Munafo, Hypercalc - The Calculator That Doesn't Overflow.
• Robert P. Munafo, Sequence A092188, Smallest Positive Integer M such that 2^3^4^5^...^N = M mod N.
• Robert G. Wilson v, Mathematica coding for "SuperPowerMod" from Vardi.
• Wolfram cloud Function Repository, PowerTowerMod.

Crossrefs

Cf. A000040, A092188, A133612, A171881, A171882, A213013, A336111, A342176.

Programs

Mathematica

a[n_] := Switch[ Mod[ Prime[n], 10], 1, 1, 3, If[ Mod[ Prime[n -1], 4] == 1, 3, 7], 5, 5, 7, If[ Mod[ Prime[n -1], 4] == 1, 7, 3], 9, 9]; a[1] = 2; a[2] = 9; Array[a, 105]
Join[{2}, Map[PowerMod[#[[2]], #[[1]], 10] &, Partition[Prime[Range[100]], 2, 1]]] (* Paolo Xausa, Jul 14 2025 *)

PARI

a(n) = if(n<2, 2, lift(Mod(prime(n),10)^prime(n-1))) \\ Hugo Pfoertner, Jul 07 2024

Formula

a(n) = A078422(n-1) mod 10. - R. J. Mathar, Jul 14 2025