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A276676 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).

%I A276676 #21 Oct 13 2016 09:42:12
%S A276676 2,11,2,47,47,2,47,47,11,2,47,47,17,17,2,683,683,683,683,683,2,683,
%T A276676 683,683,683,683,11,2,683,683,683,683,683,17,17,2,683,683,683,683,683,
%U A276676 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 A276676 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 A276676 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 A276676 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 A276676 Triangle begins
%e A276676 2;
%e A276676 11,2;
%e A276676 47,47,2;
%e A276676 47,47,11,2;
%e A276676 47,47,17,17,2;
%e A276676 683,683,683,683,683,2;
%e A276676 683,683,683,683,683,11,2;
%e A276676 683,683,683,683,683,17,17,2;
%e A276676 683,683,683,683,683,467,467,467,2;
%e A276676 683,683,683,683,683,467,467,467,11,2;
%e A276676 683,683,683,683,683,467,467,467,79,79,2;
%e A276676 683,683,683,683,683,467,467,467,79,79,17,2;
%e A276676 683,683,683,683,683,467,467,467,79,79,41,41,2;
%e A276676 683,683,683,683,683,467,467,467,79,79,41,41,11,2;
%e A276676 683,683,683,683,683,467,467,467,79,79,41,41,17,17,2;
%e A276676 683,683,683,683,683,467,467,467,107,107,107,107,107,107,107,2;
%e A276676 683,683,683,683,683,467,467,467,107,107,107,107,107,107,107,11,2;
%e A276676 The first column forms A229019.
%t A276676 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 A276676 Cf. A159559, A229019 (the first column), A229132.
%K A276676 nonn,tabl
%O A276676 2,1
%A A276676 _Vladimir Shevelev_, Sep 13 2016
%E A276676 More terms from _Peter J. C. Moses_, Sep 13 2016