A332055 Tower of 8's modulo n.

0, 0, 1, 0, 1, 4, 1, 0, 1, 6, 3, 4, 1, 8, 1, 0, 1, 10, 11, 16, 1, 14, 6, 16, 6, 14, 19, 8, 20, 16, 8, 0, 25, 18, 1, 28, 26, 30, 1, 16, 10, 22, 35, 36, 1, 6, 25, 16, 8, 6, 1, 40, 28, 46, 36, 8, 49, 20, 4, 16, 34, 8, 1, 0, 1, 58, 24, 52, 52, 36, 8, 64, 8, 26, 31

Offset

1,6

Comments

a(n) = (8^(8^(8^(8^ ... )))) mod n, provided sufficient 8'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..75.

Formula

a(n) = 8^(A000010(n) + a(A000010(n))) mod n.

a(n) = (8^^k) mod n, if n < A246496(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=8^b-floor((8^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, A246496, A332054.

Sequence in context: A010639 A035588 A318623 * A073027 A370073 A278986

Adjacent sequences: A332052 A332053 A332054 * A332056 A332057 A332058

Keyword

nonn

Author

Jinyuan Wang, Mar 04 2020

Status

approved