cp's OEIS Frontend

A130281 Integers n > 1 such that A130280(4n^2) < n, i.e., there is an m < n, m > 1 such that 4n^2(m^2 - 1) + 1 is a square.

%I A130281 #8 Aug 20 2024 15:27:00
%S A130281 28,102,248,390,490,852,1358,2032,2898,3465,3980,5302,5432,6888,8762,
%T A130281 10948,13470,15372,16352,19618,23292,27398,31960,37002,42548,48015,
%U A130281 48622,55248,62450,70252,75658,78678,87752,97498
%N A130281 Integers n > 1 such that A130280(4n^2) < n, i.e., there is an m < n, m > 1 such that 4n^2(m^2 - 1) + 1 is a square.
%C A130281 If n>4 is an even square, n=4k^2, then A130280(n) <= k since n(k^2-1)+1 = (2k^2-1)^2. This sequence lists those k for which we have strict inequality. Most terms in this sequence belong to the subsequence b(m)=2m*(2m^2-1), m>1, for which A130280(4 b(m)^2) <= m < b(m), since 4 b(m)^2(m^2-1)+1 = (8m^4-8m^2+1)^2. For other terms k of this sequence (e.g., the subsequence 390, 3465, 15372, 48015, ...), A130280(4k^2) is even smaller.
%o A130281 (PARI) checkA130281(n)={local(m=4*n^2);for(i=2,sqrt(n),if(issquare(m*(i^2-1)+1),return(i)))}
%o A130281 for(n=1,99999,if(checkA130281(n),print(n", ")))
%Y A130281 Cf. A130280.
%K A130281 nonn
%O A130281 1,1
%A A130281 _M. F. Hasler_, May 20 2007