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A110975 Numbers n such that 2*prime(n) - prime(n+1) is a square. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
KEYWORD
nonn
AUTHOR
Giovanni Teofilatto, Sep 28 2005
EXTENSIONS
Corrected and extended by Ray Chandler, Oct 07 2005
STATUS
approved

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Last modified February 24 05:49 EST 2024. Contains 370293 sequences. (Running on oeis4.)