A090783 a(n) can be expressed as the difference of the squares of consecutive primes in just three distinct ways.

1848, 6888, 14280, 16008, 19152, 36120, 112728, 116832, 129480, 139080, 176520, 190632, 190968, 199752, 216840, 236208, 252120, 274848, 303960, 314160, 340368, 363720, 435792, 458280, 503160, 513240, 686160, 688680, 698880, 712680, 721560

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 3091 terms from Robert Israel)

Example

1848 = 463^2 - 461^2 = 233^2 - 229^2 = 157^2 - 151^2.

Maple

N:= 10^6: # to get all terms <= N
V:= Vector(N/4):
p:= 3:
while p < N/2 do
  q:= p;
  p:= nextprime(p);
  r:= (p^2-q^2)/4;
  if r <= N/4 then
    V[r]:= V[r]+1
  fi
od:
map(`*`, select(t -> V[t]=3, [$1..N/4]), 4); # Robert Israel, Aug 13 2018

Prog

(PARI) is(n) = my(i=0, v=[]); forprime(p=5, n, v=[precprime(p-1), p]; if(v[2]^2-v[1]^2==n, i++)); i==3 \\ Felix Fröhlich, Aug 13 2018

Crossrefs

Cf. A078667, A090784, A090785, A091878.

Sequence in context: A094377 A080395 A092003 * A247724 A236030 A237892

Adjacent sequences: A090780 A090781 A090782 * A090784 A090785 A090786

Keyword

nonn

Author

Ray G. Opao, Feb 08 2004

Extensions

More terms from Ray Chandler, Feb 11 2004

Status

approved