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

2,1

Links

Table of n, a(n) for n=2..67.

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.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A329941 A347121 A341512 * A077805 A344539 A342043

Adjacent sequences: A276673 A276674 A276675 * A276677 A276678 A276679

Keyword

nonn,tabl

Author

Vladimir Shevelev, Sep 13 2016

Extensions

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

Status

approved