A285743 a(0) = 0, a(1) = 1; a(2*n) = prime(a(n)), a(2*n+1) = prime(a(n)+a(n+1)).

0, 1, 2, 5, 3, 17, 11, 19, 5, 71, 59, 107, 31, 113, 67, 89, 11, 383, 353, 733, 277, 983, 587, 787, 127, 827, 617, 1069, 331, 911, 461, 541, 31, 2707, 2647, 5573, 2381, 8713, 5557, 8017, 1787, 10271, 7753, 13187, 4273, 11383, 6037, 7129, 709, 7529, 6353, 12049, 4549, 14389, 8581, 11657, 2221, 10111, 7109, 11353, 3259

Offset: 0

Author

Ilya Gutkovskiy, Apr 25 2017

Keywords

• nonn
• look

Comments

A variation on Stern's diatomic sequence (A002487) and primeth recurrence (A007097).

Examples

			a(0) = 0;
a(1) = 1;
a(2) = a(2*1) = prime(a(1)) = prime(1) = 2;
a(3) = a(2*1+1) = prime(a(1)+a(2)) = prime(3) = 5;
a(4) = a(2*2) = prime(a(2)) = prime(2) = 3;
a(5) = a(2*2+1) = prime(a(2)+a(3)) = prime(7) = 17, etc.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..500
• Michael Gilleland, Some Self-Similar Integer Sequences
• Eric Weisstein's World of Mathematics, Stern's Diatomic Series
• Index entries for sequences related to Stern's sequences

Crossrefs

Cf. A002487, A007097, A082096, A259622, A285742.

Programs

Maple

A[0]:= 0: A[1]:= 1:
for n from 1 to 50 do
  A[2*n]:= ithprime(A[n]);
  A[2*n+1]:= ithprime(A[n]+A[n+1]);
od:
seq(A[i],i=0..101); # Robert Israel, Apr 25 2017

Mathematica

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], Prime[a[n/2]], Prime[a[(n - 1)/2] + a[(n + 1)/2]]]; Table[a[n], {n, 0, 60}]