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A270189 Numbers n for which (prime(n+1)-prime(n)) is not a multiple of three.

%I A270189 #17 Mar 20 2016 12:55:31
%S A270189 1,2,3,4,5,6,7,8,10,12,13,14,17,19,20,22,24,25,26,27,28,29,30,31,33,
%T A270189 34,35,38,41,42,43,44,45,48,49,50,52,53,57,59,60,61,62,63,64,65,66,68,
%U A270189 69,70,72,75,77,78,79,80,81,82,83,85,87,88,89,90,92,93,94,95,98,101,104,106,109,112,113,115,116,117,120,122,124,125
%N A270189 Numbers n for which (prime(n+1)-prime(n)) is not a multiple of three.
%C A270189 See A269364 for the effect of the bias that favors these terms over the terms of A270190.
%H A270189 Antti Karttunen, <a href="/A270189/b270189.txt">Table of n, a(n) for n = 1..10000</a>
%H A270189 Terence Tao, <a href="https://terrytao.wordpress.com/2016/03/14/biases-between-consecutive-primes/">Biases between consecutive primes</a>, blog entry March 14, 2016
%F A270189 Other identities. For all n >= 1:
%F A270189 A269849(a(n)) = n.
%t A270189 Select[Range@ 125, Mod[Prime[# + 1] - Prime@ #, 3] != 0 &] (* _Michael De Vlieger_, Mar 17 2016 *)
%o A270189 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A270189 (define A270189 (NONZERO-POS 1 1 A137264))
%o A270189 (PARI) isok(n) = ((prime(n+1) - prime(n)) % 3) != 0; \\ _Michel Marcus_, Mar 17 2016
%Y A270189 Complement: A270190.
%Y A270189 Disjoint union of A270191 and A270192.
%Y A270189 Positions of 1's and 2's in A137264.
%Y A270189 Left inverse: A269849.
%Y A270189 Cf. A000040, A001223, A269364, A269389.
%K A270189 nonn
%O A270189 1,2
%A A270189 _Antti Karttunen_, Mar 16 2016