A067805 Numbers n such that the area of the parallelogram formed by the vectors (n, prime(n)) and (n+1, prime(n+1)) is an integer square, i.e., Det[{{n, prime(n)},{n+1, prime(n+1)}}] is an integer square.

2, 3, 4, 19, 22, 53, 91, 239, 240, 266, 759, 842, 853, 915, 1000, 1801, 2016, 2230, 2724, 2782, 2908, 2944, 3323, 3347, 3938, 3984, 4027, 4070, 4529, 5828, 6228, 6914, 8739, 8774, 8861, 8930, 9320

Offset

1,1

Links

Table of n, a(n) for n=1..37.

Example

Det[{4, prime(4)}, {5, prime(5)}] = Det[{4,7}, {5,11}] = 44 - 35 = 9, an integer square, so 4 is a term of the sequence.

Mathematica

Select[Range[10^4], IntegerQ[Sqrt[Det[{{#, Prime[ # ]}, {# + 1, Prime[ # + 1]}}]]] &]

Crossrefs

Sequence in context: A265367 A265902 A245453 * A092837 A058772 A227941

Adjacent sequences: A067802 A067803 A067804 * A067806 A067807 A067808

Keyword

nonn

Author

Joseph L. Pe, Feb 07 2002

Status

approved