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A225078 Numbers n such that n^2+1 and (n+1)^2-2 are both prime. 1
1, 2, 4, 6, 14, 20, 26, 36, 54, 74, 116, 120, 126, 130, 134, 160, 176, 204, 210, 230, 236, 256, 264, 284, 300, 314, 340, 386, 420, 440, 466, 490, 496, 544, 594, 636, 644, 714, 750, 760, 784, 816, 930, 950, 986, 1070, 1124, 1140, 1146, 1156, 1174, 1176, 1210 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Prime limits of the Legendré conjecture for a given n.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Legendre's Conjecture

Wikipedia, Legendre's conjecture

EXAMPLE

n=2; n+1=3 ;n^2+1=5 and (n+1)^2-2=7.

n=490; n+1=491; n^2+1=240101 and (n+1)^2-2=241079.

MATHEMATICA

Select[Range[2000], PrimeQ[#^2 + 1] && PrimeQ[(# + 1)^2 - 2] &] (* T. D. Noe, May 06 2013 *)

PROG

(TI-BASIC) ClrIO:Input "n", n:Lbl colorin:if isPrime(n^2+1) and

isPrime((n+1)^2-2) Then:Disp n:Pause:Endif:n+1(sto)n:Goto colorin:EndPrgm

(Haskell)

import Data.Function (on)

import Data.List (elemIndices)

a225078 n = a225078_list !! (n-1)

a225078_list = elemIndices 1 $

   zipWith ((*) `on` a010051') a002522_list a008865_list

-- Reinhard Zumkeller, May 06 2013

CROSSREFS

Cf. A002522, A008865, A010051, A014085, A002496, A028871.

Sequence in context: A095698 A277909 A064409 * A032353 A062112 A226302

Adjacent sequences:  A225075 A225076 A225077 * A225079 A225080 A225081

KEYWORD

nonn

AUTHOR

César Aguilera, Apr 26 2013

STATUS

approved

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)