A110975 Numbers n such that 2*prime(n) - prime(n+1) is a square.

1, 2, 5, 6, 11, 24, 49, 50, 73, 87, 182, 183, 202, 203, 307, 309, 379, 458, 459, 520, 677, 961, 1001, 1475, 1618, 1619, 1769, 2089, 2427, 2428, 3303, 3378, 4090, 4397, 4944, 5444, 5969, 6496, 6497, 7653, 8557, 8871, 8873, 9091, 9526, 10524, 11580, 11824

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Maple

Res:= NULL:  p:= 2; count:= 0:
for n from 1 while count < 100 do
  q:= p; p:= nextprime(p);
  if issqr(2*q-p) then count:= count+1; Res:= Res, n; fi
od:
Res; # Robert Israel, Mar 02 2020

Mathematica

Select[Range[12000], IntegerQ[(2Prime[ # ] - Prime[ # + 1])^(1/2)] &] (* Ray Chandler, Oct 07 2005 *)
Position[2#[[1]]-#[[2]]&/@Partition[Prime[Range[12000]], 2, 1], _?(IntegerQ[ Sqrt[#]]&)]//Flatten (* Harvey P. Dale, Apr 30 2019 *)

Crossrefs

Cf. A110970.

Sequence in context: A255310 A051217 A275522 * A190120 A069789 A332683

Adjacent sequences: A110972 A110973 A110974 * A110976 A110977 A110978

Keyword

nonn

Author

Giovanni Teofilatto, Sep 28 2005

Extensions

Corrected and extended by Ray Chandler, Oct 07 2005

Status

approved