A214128 a(n) = 6^(6^6) mod n.

0, 0, 0, 0, 1, 0, 1, 0, 0, 6, 5, 0, 1, 8, 6, 0, 1, 0, 1, 16, 15, 16, 2, 0, 6, 14, 0, 8, 23, 6, 1, 0, 27, 18, 1, 0, 1, 20, 27, 16, 18, 36, 1, 16, 36, 2, 37, 0, 43, 6, 18, 40, 44, 0, 16, 8, 39, 52, 5, 36, 9, 32, 36, 0, 1, 60, 14, 52, 48, 36, 6, 0, 1, 38, 6, 20, 71

Offset

1,10

Comments

The indices of zeros in this sequence, i.e., divisors of 6^(6^6), are all numbers of the form 2^i * 3^j, with 0 <= i, j <= 6^6. [Edited by M. F. Hasler, Feb 25 2018]

If c and N are any positive integers, and p^k is the largest prime power divisor of c, then the divisors of c^N less than p^(k*N+1) are precisely those numbers in that range whose prime factorization includes only primes that divide c. This is the case c = 6, N = 6^6, so p^k = 2^1 = 2; so the first difference in the divisor list from A003586 is for A003586(n) = 2^(6^6+1). Franklin T. Adams-Watters, Jul 12 2012

Eventually constant: see formula. - M. F. Hasler, Feb 24 2018

If n > 1 is coprime to 6 and A000010(n) divides 6^6 then a(n)=1. - Robert Israel, Nov 27 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for eventually constant sequences.

Formula

a(n) = 0 if and only if n = 2^i 3^j, 0 <= i, j <= 6^6; after the last of these zeros at n = 6^6^6, a(n) = 6^6^6 for all n > 6^6^6 ~ 2.659*10^36305. - M. F. Hasler, Feb 24 2018

Example

a(1) = 6^(6^6) mod 1 = 0.
a(2) = 6^(6^6) mod 2 = 0.
a(3) = 6^(6^6) mod 3 = 0.
a(4) = 6^(6^6) mod 4 = 0.

Maple

seq(6 &^ (6^6) mod n, n=1..100); # Robert Israel, Nov 27 2019

Mathematica

Table[PowerMod[6, 6^6, n], {n, 100}]

Prog

(PARI) a(n)=lift(Mod(6, n)^6^6) \\ Charles R Greathouse IV, Jul 05 2012

Crossrefs

Cf. A129810 (9^9^9 mod n), A003586.

Sequence in context: A021610 A264807 A245973 * A166509 A200635 A197261

Adjacent sequences: A214125 A214126 A214127 * A214129 A214130 A214131

Keyword

nonn

Author

Marvin Ray Burns, Jul 04 2012

Status

approved