A224229 a(0)=2; for n>0, a(n) = smallest prime not occurring earlier in the sequence such that a(n-1)+a(n) is a multiple of floor(sqrt(n)). If no such prime exists, the sequence terminates.

2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 29, 37, 41, 43, 47, 61, 59, 53, 67, 73, 71, 89, 79, 97, 83, 107, 103, 127, 113, 137, 163, 157, 173, 167, 193, 197, 109, 101, 139, 131, 151, 149, 181, 179, 199, 191, 211, 227, 223, 239, 251, 281, 293, 337, 307, 379, 349, 421, 419, 449, 433, 463, 461, 491, 229, 283, 269, 331, 277, 347, 317, 443, 373, 467, 389, 499, 397, 523

Offset

0,1

Comments

Is this sequence infinite and, if so, is it a permutation of the primes? For this sequence the answers are probably both Yes. A134204 and A224223 are similar sequences whose status is also unknown, while A224221 and A224222 are similar sequences which terminate after about 20 terms.

Links

N. J. A. Sloane, Table of n, a(n) for n = 0..9999

Maple

# A224229
Digits:=100;
M1:=100000; hit:=Array(1..M1);
M2:=1000;
a:=[2]; hit[1]:=1;
p:=2;
for n from 1 to M2 do
t1:=floor(sqrt(n));
sw1:=-1;
   for i from 2 to M1  do
      q:=ithprime(i);
      if ( (p+q) mod t1 ) = 0 and hit[i] <> 1 then sw1:=1; break; fi;
   od:
if sw1 < 0 then lprint("ERROR", n, a); break; fi;
a:=[op(a), q];
hit[i]:=1;
p:=q;
                  od:
a;

Crossrefs

Cf. A134204, A224221, A224222, A224223.

Sequence in context: A342063 A067903 A341934 * A358798 A102348 A161929

Adjacent sequences: A224226 A224227 A224228 * A224230 A224231 A224232

Keyword

nonn,look

Author

N. J. A. Sloane, Apr 10 2013

Status

approved