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).

2, 11, 2, 47, 47, 2, 47, 47, 11, 2, 47, 47, 17, 17, 2, 683, 683, 683, 683, 683, 2, 683, 683, 683, 683, 683, 11, 2, 683, 683, 683, 683, 683, 17, 17, 2, 683, 683, 683, 683, 683, 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

Offset: 2

Author

Vladimir Shevelev, Sep 13 2016

Keywords

• nonn
• tabl

Examples

			Triangle begins
2;
11,2;
47,47,2;
47,47,11,2;
47,47,17,17,2;
683,683,683,683,683,2;
683,683,683,683,683,11,2;
683,683,683,683,683,17,17,2;
683,683,683,683,683,467,467,467,2;
683,683,683,683,683,467,467,467,11,2;
683,683,683,683,683,467,467,467,79,79,2;
683,683,683,683,683,467,467,467,79,79,17,2;
683,683,683,683,683,467,467,467,79,79,41,41,2;
683,683,683,683,683,467,467,467,79,79,41,41,11,2;
683,683,683,683,683,467,467,467,79,79,41,41,17,17,2;
683,683,683,683,683,467,467,467,107,107,107,107,107,107,107,2;
683,683,683,683,683,467,467,467,107,107,107,107,107,107,107,11,2;
The first column forms A229019.
		

Links

• V. Shevelev, Several results on sequences which are similar to the positive integers, arXiv:0904.2101 [math.NT], 2009.
• Vladimir Shevelev, Peter J. C. Moses, Constellations of primes generated by twin primes, arXiv:1610.03385 [math.NT], 2016.

Crossrefs

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

Programs

Mathematica

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 *)

Extensions

More terms from Peter J. C. Moses, Sep 13 2016