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A086135 Numbers n such that n and n+10 are both prime but are non-consecutive; which means that at least one prime is between n and n+10; it is not identical with A023303 because here the terms of A031928 are missing.

%I A086135 #11 Oct 25 2020 15:37:34
%S A086135 3,7,13,19,31,37,43,61,73,79,97,103,127,157,163,223,229,271,307,349,
%T A086135 373,379,433,439,457,499,607,643,673,733,751,853,877,937,967,1009,
%U A086135 1087,1093,1213,1279,1291,1297,1423,1429,1483,1489,1543,1549,1597,1609,1657,1777
%N A086135 Numbers n such that n and n+10 are both prime but are non-consecutive; which means that at least one prime is between n and n+10; it is not identical with A023303 because here the terms of A031928 are missing.
%H A086135 Harvey P. Dale, <a href="/A086135/b086135.txt">Table of n, a(n) for n = 1..1000</a>
%F A086135 Complement of a=A031928 with respect to b=A023303: [b]&[nota]: this and A031928 are disjoint, but A031928 is a proper subset of A023303.
%e A086135 First deviation from A023303 = {3,7,13,19,31,37,43,61,73,79,97,103,127,139,157,..} is due to the absence of 139=A031928(1).
%t A086135 Do[s=Prime[n]; s1=Prime[n+1]; If[PrimeQ[s+d]&& !Equal[s1-s, d], Print[s]], {n, 1, 1000}]
%t A086135 Select[Prime[Range[300]],PrimeQ[#+10]&&NextPrime[#]!=(#+10)&] (* _Harvey P. Dale_, Oct 25 2020 *)
%K A086135 nonn
%O A086135 1,1
%A A086135 _Labos Elemer_, Jul 28 2003