login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
OFFSET
1,1
COMMENTS
Note that Q-P=3(q-p).
No common terms with A181848.
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 A358399 A231440
KEYWORD
nonn
AUTHOR
Zak Seidov, Aug 18 2012
STATUS
approved