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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 18 01:03 EDT 2021. Contains 347498 sequences. (Running on oeis4.)