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 A373947 #8 Jun 30 2024 09:10:10 %S A373947 1,2,1,2,1,2,3,1,3,2,1,2,3,1,3,2,1,3,2,3,4,2,1,2,1,2,7,2,3,1,5,1,3,2, %T A373947 3,1,5,1,2,1,6,2,1,2,3,1,5,3,1,3,2,1,5,7,2,1,2,7,3,5,1,2,3,4,3,2,3,4, %U A373947 2,4,5,1,5,1,3,2,3,4,2,1,2,6,4,2,4,2,3 %N A373947 Halved and run-compressed first differences of consecutive odd primes. %C A373947 We define the run-compression of a sequence to be the anti-run obtained by reducing each run of repeated parts to a single part. Alternatively, run-compression removes all parts equal to the part immediately to their left. For example, (1,1,2,2,1) has run-compression (1,2,1). %F A373947 a(n) = A037201(n+1)/2. %e A373947 The odd primes begin: %e A373947 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, ... %e A373947 with differences: %e A373947 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, ... %e A373947 with run-compression: %e A373947 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, ... %e A373947 which is 2*a(n). %t A373947 First/@Split[Differences[Select[Range[3,100],PrimeQ]]]/2 %Y A373947 Half of A037201(n+1). %Y A373947 Run-compression of A001223. %Y A373947 A003242, A114901, A116608, A116861, A238279, A240085, A333755, A373948, A373949, A373951, A373953, A373954. %K A373947 nonn %O A373947 1,2 %A A373947 _Gus Wiseman_, Jun 29 2024