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A224223 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 n^2. If no such prime exists, the sequence terminates. 3

%I

%S 2,3,5,13,19,31,41,449,127,197,103,139,149,1879,277,173,83,5119,389,

%T 1777,223,659,1277,839,313,937,1091,367,1201,5527,773,4993,1151,7561,

%U 2843,4507,677,4799,977,5107,4493,15679,7253,26029,3011,1039,5309,3527

%N 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 n^2. If no such prime exists, the sequence terminates.

%C Is this sequence infinite and, if so, is it a permutation of the primes? The answers are probably Yes and No (7 has not appeared after 10000 terms). Compare A134204.

%H N. J. A. Sloane, <a href="/A224223/b224223.txt">Table of n, a(n) for n = 0..9999</a>

%Y Cf. A134204, A224221, A224222, A224229.

%K nonn,look

%O 0,1

%A _Daniel Drucker_ and _N. J. A. Sloane_, Apr 05 2013

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Last modified February 5 23:07 EST 2023. Contains 360091 sequences. (Running on oeis4.)