OFFSET
2,1
COMMENTS
All positive terms of the sequence are prime.
Conjecture: all terms are positive.
LINKS
V. Shevelev, Several results on sequences which are similar to the positive integers, arXiv:0904.2101 [math.NT], 2009.
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Sep 11 2013
EXTENSIONS
More terms from Alois P. Heinz, Sep 15 2013
STATUS
approved