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

1,2

Comments

Each term is the sum of two oblong numbers and therefore even.

Links

Table of n, a(n) for n=1..58.

Example

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.

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 *)

Crossrefs

Cf. A000290, A002313, A005843, A045637.

Sequence in context: A280867 A111058 A063622 * A280252 A013654 A359964

Adjacent sequences: A162149 A162150 A162151 * A162153 A162154 A162155

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 26 2009, Jul 29 2009

Extensions

Duplicates of 212 and 432 removed, 500 removed by R. J. Mathar, Sep 11 2009

Status

approved