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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. 0

%I

%S 2,3,4,19,22,53,91,239,240,266,759,842,853,915,1000,1801,2016,2230,

%T 2724,2782,2908,2944,3323,3347,3938,3984,4027,4070,4529,5828,6228,

%U 6914,8739,8774,8861,8930,9320

%N 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.

%e 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.

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

%K nonn

%O 1,1

%A _Joseph L. Pe_, Feb 07 2002

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Last modified October 21 03:38 EDT 2021. Contains 348141 sequences. (Running on oeis4.)