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A236461 Sum of two consecutive primes that is also sum of two consecutive even positive squares. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 10:39 EST 2022. Contains 350607 sequences. (Running on oeis4.)