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 A381616 #10 Mar 03 2025 13:28:48 %S A381616 7643,31,3517,1049,2,41,173,401,523,113,337,449,6599,251,1993,2543, %T A381616 743,593,1481,1301,1069,2357,17657,4079,2797,8219,64123,81299,19289, %U A381616 40129,6709,13999,4271,1669,37579,28793,38039,12413,125711,24907,3181,41597,27253 %N A381616 a(n) is the smallest prime that starts the first occurrence of exactly n consecutive primes in A381019. %C A381616 As the sequence grows, increasingly longer chains of consecutive prime numbers begin to appear. %C A381616 Conjecture: a(n) always exists. %e A381616 For n = 2, we observe that 9, 31, 37, and 8 are four consecutive terms of A381019, where 31 and 37 are exactly two consecutive primes and represent the first occurrence of two consecutive terms that are prime. So, a(2) = 31. %Y A381616 Cf. A381019, A381117. %K A381616 nonn %O A381616 1,1 %A A381616 _Gonzalo MartÃnez_, Mar 01 2025