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
Keywords
Examples
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.
Programs
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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 *) -
PARI
a(n) = {k=1; while( gcd(5^n-1, k^n-1)!=1, k++); k; } -
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]])
Extensions
a(60) from Harvey P. Dale, Jul 29 2024
Comments