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 A193746 Smallest k such that k*n^2 +1 is an n-th power. 4

%I #13 Aug 27 2020 05:41:21

%S 1,2,7,5,311,434,42799,90075,12345679,34867844,6140565047,1695421,

%T 4696537119847,20088655029078,5124095576030431,25657845139503479,

%U 7563707819165039903,43404581642184336392,14523213296398891966759

%N Smallest k such that k*n^2 +1 is an n-th power.

%e a(9) = 12345679 because 12345679*9^2+1 = 1000000000 = 10^9.

%t a={}; Do[k = 2;While[ !IntegerQ[(k^n - 1)/n^2], k++ ]; AppendTo[a,(k^n-1)/n^2], {n, 1, 20}]; a

%o (PARI) a(n)=my(k);while(!ispower(k++*n^2+1,n),);k \\ _Charles R Greathouse IV_, May 15 2013

%Y Cf. A076943.

%K nonn

%O 1,2

%A _Michel Lagneau_, Aug 03 2011

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Last modified September 8 22:43 EDT 2024. Contains 375759 sequences. (Running on oeis4.)