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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
47, 257, 607, 619, 647, 1097, 1459, 1499, 1709, 1747, 1889, 2677, 2861, 3307, 3559, 4007, 5107, 5387, 5419, 6317, 6367, 7309, 7829, 9467, 10079, 10639, 11789, 12589, 12647, 12721, 13457, 14747, 15149, 15749, 15797, 15889, 15907, 17477, 17839, 18217, 19477 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

No common terms with A181848.

LINKS

Zak Seidov, Table of n, a(n) for n = 1..1000

EXAMPLE

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

MATHEMATICA

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]]

Transpose[Select[Partition[Prime[Range[2500]], 2, 1], AllTrue[{2#[[1]]- #[[2]], 2#[[2]]-#[[1]]}, PrimeQ]&]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 14 2015 *)

CROSSREFS

Cf. A181848.

Sequence in context: A142084 A140850 A078965 * A142119 A231440 A142164

Adjacent sequences:  A186166 A186167 A186168 * A186170 A186171 A186172

KEYWORD

nonn

AUTHOR

Zak Seidov, Aug 18 2012

STATUS

approved

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Last modified June 19 21:32 EDT 2021. Contains 345151 sequences. (Running on oeis4.)