A229019 Minimal position at which the sequence defined in the same way as A159559 but with initial term prime(n) merges with A159559; a(n)=0 if there is no such position.

2, 11, 47, 47, 47, 683, 683, 683, 683, 683, 683, 683, 683, 683, 683, 683, 683, 1117, 1117, 1117, 1117, 1117, 1117, 1117, 1117, 1117, 1117, 1117, 6257, 6257, 6257, 6257, 6257, 6257, 6257, 6257, 390703, 390703, 390703, 390703, 390703, 390703, 390703, 390703

Offset: 2

Author

Vladimir Shevelev, Sep 11 2013

Keywords

• nonn

Comments

All positive terms of the sequence are prime.

Conjecture: all terms are positive.

Examples

			For n>=2, denote by A_n the sequence defined in the same way as A159559 but with initial term A_n(2)=prime(n). In case n=2 A_2(2)=3, hence A_2 = A159559, and so a(2)=2. Suppose n=3. Then A_3(2)=5 and by the definition of A159559 we have A_3(3)=7, A_3(4)=8, A_3(5)=11, A_3(6)=12, A_3(7)=13, A_3(8)=14, A_3(9)=15, A_3(10)=16, A_3(11)=17. Since A159559(11) is also 17, then, beginning with 11, A_3 merges with A159559 and a(3)=11. - _Vladimir Shevelev_, Sep 11 2016.
		

Links

• V. Shevelev, Several results on sequences which are similar to the positive integers, arXiv:0904.2101 [math.NT], 2009.

Crossrefs

Cf. A159559, A159698.

Programs

Maple

b:= proc(n, p) option remember; local m;
      if n=2 then p
    else for m from b(n-1,p)+1 while isprime(m) xor isprime(n)
         do od; m
      fi
    end:
a:= proc(n) option remember; local k;
      for k from 2 while b(k, 3)<>b(k, ithprime(n)) do od; k
    end:
seq(a(n), n=2..20);  # Alois P. Heinz, Sep 15 2013

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; t = f[3, nn]; Table[1 + First@ Flatten@ Position[BitXor[t, f[Prime@ n, nn]], 0], {n, 2, 37}] (* Michael De Vlieger, Sep 13 2016, after Peter J. C. Moses at A159559 *)

Extensions

More terms from Alois P. Heinz, Sep 15 2013