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.

28, 102, 248, 390, 490, 852, 1358, 2032, 2898, 3465, 3980, 5302, 5432, 6888, 8762, 10948, 13470, 15372, 16352, 19618, 23292, 27398, 31960, 37002, 42548, 48015, 48622, 55248, 62450, 70252, 75658, 78678, 87752, 97498

Offset: 1

Author

M. F. Hasler, May 20 2007

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A130280.

Programs

PARI

checkA130281(n)={local(m=4*n^2);for(i=2,sqrt(n),if(issquare(m*(i^2-1)+1),return(i)))}
for(n=1,99999,if(checkA130281(n),print(n", ")))