A162152 Numbers of the form x(x-1) + y(y-1) with x^2 + y^2 being a prime, x,y >= 0.
0, 2, 8, 12, 22, 30, 32, 44, 50, 62, 76, 84, 90, 96, 98, 122, 132, 140, 158, 162, 174, 182, 212, 222, 240, 246, 254, 260, 274, 288, 292, 312, 326, 328, 348, 362, 372, 380, 386, 392, 404, 422, 432, 482, 490, 510, 524, 536, 552, 562, 572, 578, 582, 612, 618, 630, 638, 650
Offset: 1
Keywords
Examples
a(1)=0 from x=y=1, with 2 a prime. a(2)=2 from x=1, y=2, with 5 a prime. a(3)=8 from x=2, y=3, with 13 a prime. a(4)=12 from x=1, y=4, with 17 a prime. a(4)=22 from x=2, y=5, with 29 a prime. a(.)=212 from x=2, y=15, with 229 a prime, or from x=8, y=13, with 233 a prime.
Programs
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Maple
obl := proc(n) n*(n-1) ; end: lim := 800; L := {} ; for x from 0 to lim/2 do for y from x to lim/2 do if obl(x)+obl(y) <= lim then if isprime(x^2+y^2) then L := L union { obl(x)+obl(y) } ; fi; fi; od: od: sort(L) ; # R. J. Mathar, Sep 11 2009 -
Mathematica
Take[#[[1]](#[[1]]-1)+#[[2]](#[[2]]-1)&/@Select[Tuples[ Range[ 0,40],2],PrimeQ[ Total[#^2]]&]//Union,60] (* Harvey P. Dale, Jun 07 2020 *)
Extensions
Duplicates of 212 and 432 removed, 500 removed by R. J. Mathar, Sep 11 2009
Comments