A236461 Sum of two consecutive primes that is also sum of two consecutive even positive squares.

52, 100, 340, 1460, 2452, 2740, 4420, 20404, 21220, 36452, 48052, 62660, 66980, 94180, 103060, 108580, 128020, 140452, 142580, 169364, 171700, 195940, 221780, 254900, 260644, 361252, 378452, 490052, 498004, 717604, 736900, 756452, 766324, 791284, 879140, 889780, 916660, 1016740, 1104100, 1164340, 1232452, 1283204

Offset: 1

Author

Zak Seidov, Jan 26 2014

Keywords

• nonn

Comments

All values of (q - p) are multiples of 6.

m = p + q = x^2 + (x+2)^2; {m,p,q,x}: {52, 23, 29, 4}, {100, 47, 53, 6}, {340, 167, 173, 12}, {1460, 727, 733, 26}, {2452, 1223, 1229, 34}, {2740, 1367, 1373, 36}, {4420, 2207, 2213, 46}.

Intersection of A001043 and A108099. - Michel Marcus, Jan 27 2014

Examples

			52 = 23 + 29 = 4^2 + 6^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001043, A108099.

Programs

Maple

count:= 0: R:= NULL:
for m from 1 while count < 100 do
  y:= 8*m^2+8*m+4;
  if prevprime(y/2) + nextprime(y/2)=y then
     count:= count+1;
     R:= R, y;
  fi
od:
R; # Robert Israel, Jan 07 2020

Mathematica

With[{nn=100000},Intersection[Total/@Partition[Prime[Range[nn]],2,1],Total/@ Partition[Range[2,2nn,2]^2,2,1]]] (* Harvey P. Dale, Jul 03 2021 *)

PARI

v=vector(1300000); pp=3; forprime(p=5,#v/2,v[p+pp]++;pp=p);forstep(k=2,sqrtint(#v/2)-1,2,v[2*(k^2+2*k+2)]++);for(k=1,#v,if(v[k]==2,print1(k,", "))) \\ Hugo Pfoertner, Jan 07 2020