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Conjecture: each term > 3 of the sequence is the greater member of a twin prime pair (A006512).
Indices of the records are 1, 2, 4, 6, 9, 10, 15, 18, 21, 25, 28, 30, 38, 72, 90, ... [R. J. Mathar, Nov 05 2009]
Tally[A167494][[All, 1]] //. {a1___, a2_, a3___, a4_, a5___} /; a4 <= a2 :> {a1, a2, a3, a5} (* Jean-François Alcover, Oct 29 2018, using Harvey P. Dale 's code for A167494 *)
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Simplified the definition to include all records; one term added - _by _R. J. Mathar_, Nov 05 2009
Terms a(16) to a(21) from R. J. Mathar, Nov 19 2009
Term a(22) from Jean-François Alcover, Oct 29 2018
Indices of the records are 1, 2, 4, 6, 9, 10, 15, 18, 21, 25, 28, 30, 38, 72, 90,... [_R. J. Mathar, _, Nov 05 2009]
One can formulate a similar conjecture without verification of the primality of the terms (see Conjecture 4 in my paper). [From __Vladimir Shevelev_, Nov 13 2009]
E. S. Rowland, <a href="httphttps://www.cs.uwaterloo.ca/journals/JIS/VOL11/Rowland/rowland21
E. S. Rowland, <a href="httphttps://arXivarxiv.org/abs/0710.3217">A natural prime-generating recurrence</a>, arXiv:0710.3217 [math.NT], 2007-2008.
V. Shevelev, <a href="httphttps://arXivarxiv.org/abs/0910.4676">A new generator of primes based on the Rowland idea</a>, arXiv:0910.4676 [math.NT], 2009.
V. Shevelev, <a href="httphttps://arXivarxiv.org/abs/math.0911.5478">Three theorems on twin primes</a> , arXiv:0911.5478 [math.NT], 2009-2010. [From __Vladimir Shevelev_, Dec 03 2009]
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