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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 12 21:10 EDT 2020. Contains 336440 sequences. (Running on oeis4.)