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Triangle read by rows: T(n,k) (n>=2, k=2,...,n) is the minimal position at which the sequence A_n merges with the sequence A_k, where A_n be the sequence defined in the same way as A159559 but with initial term prime(n).
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%I #21 Oct 13 2016 09:42:12

%S 2,11,2,47,47,2,47,47,11,2,47,47,17,17,2,683,683,683,683,683,2,683,

%T 683,683,683,683,11,2,683,683,683,683,683,17,17,2,683,683,683,683,683,

%U 467,467,467,2,683,683,683,683,683,467,467,467,11,2,683,683,683,683,683,467,467,467,79,79,2

%N Triangle read by rows: T(n,k) (n>=2, k=2,...,n) is the minimal position at which the sequence A_n merges with the sequence A_k, where A_n be the sequence defined in the same way as A159559 but with initial term prime(n).

%H V. Shevelev, <a href="http://arxiv.org/abs/0904.2101">Several results on sequences which are similar to the positive integers</a>, arXiv:0904.2101 [math.NT], 2009.

%H Vladimir Shevelev, Peter J. C. Moses, <a href="https://arxiv.org/abs/1610.03385">Constellations of primes generated by twin primes</a>, arXiv:1610.03385 [math.NT], 2016.

%e Triangle begins

%e 2;

%e 11,2;

%e 47,47,2;

%e 47,47,11,2;

%e 47,47,17,17,2;

%e 683,683,683,683,683,2;

%e 683,683,683,683,683,11,2;

%e 683,683,683,683,683,17,17,2;

%e 683,683,683,683,683,467,467,467,2;

%e 683,683,683,683,683,467,467,467,11,2;

%e 683,683,683,683,683,467,467,467,79,79,2;

%e 683,683,683,683,683,467,467,467,79,79,17,2;

%e 683,683,683,683,683,467,467,467,79,79,41,41,2;

%e 683,683,683,683,683,467,467,467,79,79,41,41,11,2;

%e 683,683,683,683,683,467,467,467,79,79,41,41,17,17,2;

%e 683,683,683,683,683,467,467,467,107,107,107,107,107,107,107,2;

%e 683,683,683,683,683,467,467,467,107,107,107,107,107,107,107,11,2;

%e The first column forms A229019.

%t f[n_, r_] := Block[{a}, a[2] = n; a[x_] := a[x] = If[PrimeQ@ x, NextPrime@ a[x - 1], NestWhile[# + 1 &, a[x - 1] + 1, PrimeQ@ # &]]; Map[a, Range[2, r]]]; nn = 10^4; Table[1 + First@ Flatten@ Position[BitXor[f[Prime@ n, nn], f[Prime@ k, nn]], 0], {n, 2, 12}, {k, 2, n}] // Flatten (* _Michael De Vlieger_, Sep 13 2016, after _Peter J. C. Moses_ at A159559 *)

%Y Cf. A159559, A229019 (the first column), A229132.

%K nonn,tabl

%O 2,1

%A _Vladimir Shevelev_, Sep 13 2016

%E More terms from _Peter J. C. Moses_, Sep 13 2016