Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Jul 30 2017 22:28:57
%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