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, 34072038

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.

Are all terms even? - Harvey P. Dale, Jul 29 2024

Links

Table of n, a(n) for n=1..60.

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.

Mathematica

lpi[n_]:=Module[{k=1, c=5^n-1}, While[!CoprimeQ[c, k^n-1], k++]; k]; Array[lpi, 60] (* Harvey P. Dale, Jul 29 2024 *)

Prog

(SageMath)
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 A385538 A152780

Adjacent sequences: A270357 A270358 A270359 * A270361 A270362 A270363

Keyword

nonn

Author

Tom Edgar, Mar 16 2016

Extensions

a(60) from Harvey P. Dale, Jul 29 2024

Status

approved