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

1,1

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A001043, A108099.

Sequence in context: A039475 A274338 A094552 * A044141 A044522 A335479

Adjacent sequences: A236458 A236459 A236460 * A236462 A236463 A236464

Keyword

nonn

Author

Zak Seidov, Jan 26 2014

Status

approved