This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A282323 #55 Mar 02 2024 14:11:15
%S A282323 17,107,137,197,227,347,617,827,857,1277,1427,1487,1607,1667,1697,
%T A282323 1787,1877,1997,2027,2087,2237,2267,2657,2687,3167,3257,3467,3527,
%U A282323 3557,3767,3917,4127,4157,4217,4337,4517,4547,4637,4787,4967,5417,5477,5657,5867,6197
%N A282323 Lesser of twin primes congruent to 17 (mod 30).
%C A282323 The union of [this sequence and A282324] is A132242.
%C A282323 The union of [{3, 5}, A282321, this sequence and A060229] is the lesser of twin primes sequence A001359.
%C A282323 The union of [{3, 5, 7}, A282321 to A282326] is the twin primes sequence A001097.
%C A282323 A181605 without the 7. The proof works along the same lines as the proof in A282322. - _R. J. Mathar_, Feb 14 2017
%C A282323 Number of terms < 10^k: 0, 0, 1, 9, 64, 414, 2734, 19674, 146953, ... - _Muniru A Asiru_, Jan 09 2018
%H A282323 Muniru A Asiru, <a href="/A282323/b282323.txt">Table of n, a(n) for n = 1..3000</a>
%e A282323 From _Muniru A Asiru_, Jan 25 2018: (Start)
%e A282323 17 is a member because the pair (17, 19) is a twin prime, 17 < 19 and 17 mod 30 = 17.
%e A282323 137 is a member because the pair (137, 139) is a twin prime, 137 < 139 and 137 mod 30 = 17.
%e A282323 197 is a member because the pair (197, 199) is a twin prime, 197 < 199 and 197 mod 30 = 17.
%e A282323 (End)
%p A282323 a:={}:
%p A282323 for i from 1 to 1229 do
%p A282323 if isprime(ithprime(i)+2) and ithprime(i) mod 30 = 17 then
%p A282323 a:={op(a),ithprime(i)}:
%p A282323 fi:
%p A282323 od:
%p A282323 a;
%t A282323 Select[17 + 30 Range[0, 220], PrimeQ[#] && PrimeQ[# + 2] &] (* _Robert G. Wilson v_, Jan 09 2018 *)
%t A282323 Select[Partition[Prime[Range[1000]],2,1],#[[2]]-#[[1]]==2&&Mod[#[[1]],30]==17&][[;;,1]] (* or *) Select[Range[17,7000,30],AllTrue[#+{0,2},PrimeQ]&] (* _Harvey P. Dale_, Mar 02 2024 *)
%o A282323 (Magma) [p: p in PrimesUpTo(7000) | IsPrime(p+2) and p mod 30 eq 17 ]; // _Vincenzo Librandi_, Feb 13 2017
%o A282323 (PARI) list(lim)=my(v=List(), p=2); forprime(q=3, lim+2, if(q-p==2 && q%30==19, listput(v, p)); p=q); Vec(v) \\ _Charles R Greathouse IV_, Feb 14 2017
%o A282323 (GAP)
%o A282323 P:=Filtered([1..400000], IsPrime);;
%o A282323 P1:=List(Filtered(Filtered(List([1..Length(P)-1],n->[P[n],P[n+1]]),i->i[2]-i[1]=2),j->j[1] mod 30=17),k->k[1]);; # _Muniru A Asiru_, Jul 08 2017
%Y A282323 Subset of A001097, A001359, A039949, A132242 and A132247.
%Y A282323 Cf. A006512, A232880, A232881, A232882, A282321, A282322, A282324, A282326.
%K A282323 nonn
%O A282323 1,1
%A A282323 _Martin Renner_, Feb 11 2017