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A134207 a(0) = 2; for n > 0, a(n) = the smallest prime which is > a(n-1) such that a(n-1) + a(n) is a multiple of n.

%I A134207 #16 Mar 08 2020 00:04:27
%S A134207 2,3,5,7,13,17,19,23,41,67,73,103,113,173,191,199,233,277,281,479,521,
%T A134207 571,617,809,823,827,863,919,929,1217,1303,1487,1489,1613,1753,2027,
%U A134207 2113,2179,2267,2647,2713,3109,3191,3259,3517,3593,3767,3847,3881,4057
%N A134207 a(0) = 2; for n > 0, a(n) = the smallest prime which is > a(n-1) such that a(n-1) + a(n) is a multiple of n.
%H A134207 Eric M. Schmidt, <a href="/A134207/b134207.txt">Table of n, a(n) for n = 0..1000</a>
%e A134207 The primes that are > a(8)=41 form the sequence 43,47,53,59,61,67,71,... Of these, 67 is the smallest that when added to a(8)=41 gets a multiple of 9 -- 41+67 = 108 = 9*12. (41+p is not divisible by 9 for p = any prime which is > 41 and is < 67.) So a(9) = 67.
%t A134207 a = {2}; For[n = 1, n < 100, n++, i = 1; While[Not[Mod[a[[ -1]] + Prime[PrimePi[a[[ -1]]] + i], n] == 0], i++ ]; AppendTo[a, Prime[PrimePi[a[[ -1]]] + i]]]; a (* _Stefan Steinerberger_, Oct 17 2007 *)
%o A134207 (Sage)
%o A134207 def A134207(max) :
%o A134207     res = [2]; p = 3
%o A134207     for n in range(1,max+1) :
%o A134207         while (res[n-1] + p) % n != 0 : p = next_prime(p)
%o A134207         res.append(p); p = next_prime(p)
%o A134207     return res # _Eric M. Schmidt_, May 23 2013
%Y A134207 Cf. A134204, A134208, A134209.
%K A134207 nonn
%O A134207 0,1
%A A134207 _Leroy Quet_, Oct 14 2007
%E A134207 More terms from _Stefan Steinerberger_, Oct 17 2007