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 A033448 #41 Feb 23 2025 09:59:24
%S A033448 74453,76543,132893,182243,202823,297403,358793,485923,655453,735883,
%T A033448 759113,780613,797833,849143,1260383,1306033,1442173,1531093,1534153,
%U A033448 1586953,1691033,1717063,1877243,1945763,1973633,2035513,2067083,2216803,2266993,2542513,2556803,2565203,2805773
%N A033448 Initial prime in set of 4 consecutive primes in arithmetic progression with common difference 18.
%C A033448 Up to n = 10^4, the smallest difference a(n+1) - a(n) is 60 and occurs at n = 8571. - _M. F. Hasler_, Oct 26 2018
%C A033448 Each term is congruent to 3 mod 10 (as noted by Zak Seidov in the SeqFan email list). This means the three following consecutive primes are always congruent to 1, 9, and 7 mod 10, respectively (i.e., final digits for these primes are 3, 1, 9, 7, in that order). There cannot be a set of 5 such consecutive primes because a(n) + 4*18 == 5 (mod 10) so is a multiple of 5. - _Rick L. Shepherd_, Mar 27 2023
%H A033448 M. F. Hasler, <a href="/A033448/b033448.txt">Table of n, a(n) for n = 1..10000</a>
%H A033448 <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>
%e A033448 {74453, 74471, 74489, 74507} is the first such set of 4 consecutive primes with common difference 18, so a(1) = 74453.
%t A033448 A033448 = Reap[For[p = 2, p < 2100000, p = NextPrime[p], p2 = NextPrime[p]; If[p2 - p == 18, p3 = NextPrime[p2]; If[p3 - p2 == 18, p4 = NextPrime[p3]; If[p4 - p3 == 18, Sow[p]]]]]][[2, 1]] (* _Jean-François Alcover_, Jun 28 2012 *)
%t A033448 Transpose[Select[Partition[Prime[Range[160000]],4,1],Union[ Differences[ #]] == {18}&]][[1]] (* _Harvey P. Dale_, Jun 17 2014 *)
%o A033448 (PARI) A033448(n,show_all=1,g=18,p=2,o,c)={forprime(q=p+1,,if(p+g!=p=q,next, q!=o+2*g, c=3, c++>4, print1(o-g","); n--||break); o=q-g);o-g} \\ Can be used as nxt(p)=A033448(1,,,p+1), e.g.: {p=0;vector(20,i,p=nxt(p))} or {p=0;for(i=1,1e4,write("b.txt",i" "nxt(p)))}. - _M. F. Hasler_, Oct 26 2018
%Y A033448 Analogous sequences (start of CPAP-4 with common difference in square brackets): A033451 [6], A033447 [12], A033448 [this: 18], A052242 [24], A052243 [30], A058252 [36], A058323 [42], A067388 [48], A259224 [54], A210683 [60].
%Y A033448 Cf. A033450, A052189.
%K A033448 nonn
%O A033448 1,1
%A A033448 _Jeff Burch_
%E A033448 More terms from _Labos Elemer_, Jan 31 2000
%E A033448 Definition clarified by _Harvey P. Dale_, Jun 17 2014
%E A033448 Example reflecting final digits given by _Rick L. Shepherd_, Mar 27 2023