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A166564

Twin prime pairs p, p+2 such that p+(p+2)+1 and p*(p+2)+1 are both square.

3, 5, 11, 13, 59, 61, 179, 181, 311, 313, 419, 421, 2111, 2113, 3119, 3121, 5099, 5101, 21011, 21013, 21839, 21841, 24419, 24421, 30011, 30013, 37811, 37813, 41759, 41761, 44699, 44701, 60899, 60901, 68819, 68821, 83639, 83641, 86111, 86113

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OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..600

EXAMPLE

Twin primes (3,5) are in this sequence because 3+5+1=9 and 3*5+1=16; (11,13) because 11+13+1=25 and 11*13+1=144.

MATHEMATICA

tppQ[{a_, b_}]:=IntegerQ[Sqrt[a+b+1]]&&IntegerQ[ Sqrt[a b +1]]; Flatten[Select[ Select[Partition[ Prime[Range[9000]], 2, 1], Last[#]-First[#]==2&], tppQ]] (* Harvey P. Dale, Apr 01 2011 *)

CROSSREFS

Sequence in context: A122564 A162876 A162875 * A058595 A154773 A176658

Adjacent sequences: A166561 A166562 A166563 * A166565 A166566 A166567

KEYWORD

nonn

AUTHOR

Vincenzo Librandi, Oct 25 2009

EXTENSIONS

Corrected and extended by Harvey P. Dale, Apr 01 2011.

STATUS

approved

URL: https://oeis.org/A166564

⇱ A166564 - OEIS