A270360 Least positive integer k such that 5^n-1 and k^n-1 are relatively prime.

2, 6, 2, 6, 2, 42, 2, 6, 2, 132, 2, 546, 2, 12, 6, 102, 2, 798, 2, 198, 2, 138, 2, 546, 2, 6, 2, 348, 2, 85932, 2, 102, 2, 12, 22, 383838, 2, 12, 6, 2706, 2, 1806, 2, 414, 22, 282, 2, 9282, 2, 264, 2, 318, 2, 1596, 2, 348, 2, 354, 2

Offset

1,1

Comments

Note that (5^n-1)^n-1 is always relatively prime to 5^n-1.

Based on conjecture given in A270390, a(n) = 2 infinitely often.

Links

Table of n, a(n) for n=1..59.

Example

Since 5^2-1 = 24 and 6^2-1 = 35 are relatively prime while 2^2-1, 3^2-1, 4^2-1, and 5^2-1 are not relatively prime to 24, a(5) = 3.

Prog

(Sage)
def min_k(n):
    g, k=2, 0
    while g!=1:
        k=k+1
        g=gcd(5^n-1, k^n-1)
    return k
print([min_k(n) for n in [1..60]])
(PARI) a(n) = {k=1; while( gcd(5^n-1, k^n-1)!=1, k++); k; }

Crossrefs

Cf. A260119, A268081.

Sequence in context: A232273 A307892 A276152 * A163904 A152780 A340857

Adjacent sequences: A270357 A270358 A270359 * A270361 A270362 A270363

Keyword

nonn

Author

Tom Edgar, Mar 16 2016

Status

approved