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 A290450 #51 Aug 05 2025 00:14:42
%S A290450 139,181,241,283,337,409,421,547,577,631,691,709,787,811,829,887,919,
%T A290450 1021,1039,1051,1153,1171,1249,1399,1471,1627,1637,1699,1723,1801,
%U A290450 1879,2017,2029,2053,2089,2143,2521,2647,2719,2731,2767,2887,2917,3001,3089,3109,3361,3413,3517,3547,3571
%N A290450 Primes with property that the next prime has the same last digit.
%C A290450 Starts off the same as A031928, primes p such that the next prime is p + 10. First term that differs is 887, since 897 = 3 * 13 * 23 and the next prime is 907.
%C A290450 As the primes get larger and more sparsely distributed, the difference between successive primes is less likely to be less than 10.
%C A290450 One might expect that a prime is 1/4 as likely to be followed by a prime with the same least significant digit in base 10 (since the possibilities are 1, 3, 7, 9).
%C A290450 One might also expect this sequence to consist of a quarter of the primes. And yet pi(a(50)) = pi(3547) = 497; the 200th prime is 1223.
%H A290450 Marius A. Burtea, <a href="/A290450/b290450.txt">Table of n, a(n) for n = 1..5005</a>
%H A290450 Evelyn Lamb, <a href="https://www.scientificamerican.com/article/peculiar-pattern-found-in-random-prime-numbers/">"Peculiar Pattern Found in 'Random' Prime Numbers"</a>, Nature, March 14, 2016, republished by Scientific American.
%H A290450 Robert J. Lemke Oliver and Kannan Soundararajan, <a href="https://arxiv.org/abs/1603.03720">Unexpected biases in the distribution of consecutive primes</a>, arXiv preprint arXiv:1603.03720 [math.NT], submitted on March 11, 2016.
%F A290450 A031928 UNION A031938 UNION A124596 UNION A126721 UNION ... - _R. J. Mathar_, Jan 23 2022
%e A290450 139 is in the sequence because the immediately following prime is 149, which also ends in 9.
%e A290450 But 149 is not in the sequence because the next prime after that one is 151, which ends in 1, not 9.
%t A290450 Select[Partition[Prime[Range[1000]], 2, 1], Mod[#[[1]], 10] == Mod[#[[2]], 10] &][[All, 1]] (* _Harvey P. Dale_, Aug 21 2017 *)
%t A290450 Module[{nn=1000,prs,p},prs=Prime[Range[nn]];p=Divisible[#,10]&/@ Differences[prs];Pick[Most[prs],p]] (* _Harvey P. Dale_, Aug 22 2017 *)
%o A290450 (Magma) f:=func<p,m|p mod 10 eq m and NextPrime(p) mod 10 eq m>; a:=[]; for p in PrimesUpTo(4000) do if f(p,1) or f(p,3) or f(p,7) or f(p,9) then Append(~a,p); end if; end for; a; // _Marius A. Burtea_, Oct 16 2019
%Y A290450 Cf. A031928 (subset), A050434 (with 2 digits).
%K A290450 nonn,base
%O A290450 1,1
%A A290450 _Alonso del Arte_, Aug 06 2017