A332054 Tower of 9's modulo n.

0, 1, 0, 1, 4, 3, 1, 1, 0, 9, 5, 9, 1, 1, 9, 9, 9, 9, 1, 9, 15, 5, 8, 9, 14, 1, 0, 1, 9, 9, 4, 9, 27, 9, 29, 9, 1, 1, 27, 9, 9, 15, 11, 5, 9, 31, 32, 9, 15, 39, 9, 1, 9, 27, 49, 1, 39, 9, 57, 9, 34, 35, 36, 9, 14, 27, 22, 9, 54, 29, 12, 9, 72, 1, 39, 1, 71, 27

Offset

1,5

Comments

a(n) = (9^(9^(9^(9^ ... )))) mod n, provided sufficient 9's are in the tower such that adding more doesn't affect the value of a(n).

Links

Table of n, a(n) for n=1..78.

Formula

a(n) = 9^a(A000010(n)) mod n.

a(n) = (9^^k) mod n, if n < A246497(k), where ^^ is Knuth's double-arrow notation.

Prog

(PARI) a(n) = {my(b, c=0, d=n, k=1, x=1); while(k==1, z=x; y=1; b=1; while(z>0, while(y<z, d=eulerphi(d); y++); b=9^b-floor((9^b-1)/d)*d; z=z-1; y=1; d=n); if(c==b, k=0); c=b; x++); b%n; }

Crossrefs

Cf. A240162, A245970, A245971, A245972, A245973, A245974, A246497, A332055.

Sequence in context: A354794 A355401 A195596 * A129810 A016500 A211451

Adjacent sequences: A332051 A332052 A332053 * A332055 A332056 A332057

Keyword

nonn

Author

Jinyuan Wang, Mar 03 2020

Status

approved