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 A186169 Consider two consecutive primes {p,q} such that {P=2p-q,Q=2q-p} are both prime. Sequence gives lesser primes p. 2

%I #17 Apr 14 2015 14:45:48

%S 47,257,607,619,647,1097,1459,1499,1709,1747,1889,2677,2861,3307,3559,

%T 4007,5107,5387,5419,6317,6367,7309,7829,9467,10079,10639,11789,12589,

%U 12647,12721,13457,14747,15149,15749,15797,15889,15907,17477,17839,18217,19477

%N Consider two consecutive primes {p,q} such that {P=2p-q,Q=2q-p} are both prime. Sequence gives lesser primes p.

%C Note that Q-P=3(q-p).

%C No common terms with A181848.

%H Zak Seidov, <a href="/A186169/b186169.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1)=47 because p=47, q=53 and {P=41,Q=59} are both prime.

%t a = 2; Reap[ Do[b = Prime[n]; If[PrimeQ[2*a - b] && PrimeQ[2*b - a], Sow[a]]; a = b, {n, 2, 1000}]][[2, 1]]

%t Transpose[Select[Partition[Prime[Range],2,1],AllTrue[{2#[]- #[], 2#[]-#[]},PrimeQ]&]][] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Apr 14 2015 *)

%Y Cf. A181848.

%K nonn

%O 1,1

%A _Zak Seidov_, Aug 18 2012

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Last modified June 9 23:59 EDT 2023. Contains 363183 sequences. (Running on oeis4.)