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

1,1

Comments

This sequence is not periodic.

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.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A253169 A387294 A375509 * A339925 A389490 A171052

Adjacent sequences: A373492 A373493 A373494 * A373496 A373497 A373498

Keyword

nonn

Author

Robert G. Wilson v, Jun 06 2024

Status

approved