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 A306803 #12 Dec 02 2020 03:19:36 %S A306803 0,1,3,0,4,1,5,7,2,3,0,6,8,10,11,9,4,1,13,12,5,15,17,16,7,14,18,20,19, %T A306803 21,2,3,0,22,23,6,24,25,26,28,27,29,8,30,32,31,10,34,35,33,36,11,37, %U A306803 38,9,4,1,39,41,40,13,42,43,44,46,45,47,12,5,49,50,48,51,53,52,15,54,17,55,16,7,56,58,57,14,60,59,61,18,62 %N A306803 An irregular fractal sequence: underline a(n) iff [a(n-1) + a(n)] is prime; all underlined terms rebuild the starting sequence. %C A306803 The sequence S starts with a(1) = 0 and a(2) = 1. S is extended by duplicating the first term A among the not yet duplicated terms, under the condition that [A + the last term Z of the sequence] is prime. If this is not the case, we then extend the S with the smallest integer X not yet present in S such that [X + the last term Z of the sequence] is not a prime. This is the lexicographically first sequence with this property. %H A306803 Jean-Marc Falcoz, <a href="/A306803/b306803.txt">Table of n, a(n) for n = 1..10002</a> %e A306803 S starts with a(1) = 0 and a(2) = 1 %e A306803 Can we duplicate a(1) to form a(3)? No, as a(2) + a(3) would be 1 and 1 is not prime; we thus extend S with the smallest integer X not yet in S such that [X + a(2)] is not prime. We get X = 3 and thus a(3) = 3. %e A306803 Can we duplicate a(1) to form a(4)? Yes, as now [a(1) + a(3)] is prime; we get thus a(4) = 0. %e A306803 Can we duplicate a(2) to form a(5)? No, as a(4) + a(2) would be 1 and 1 is not prime; we thus extend S with the smallest integer X not yet in S such that [X + a(4)] is not prime. We get X = 4 and thus a(5) = 4. %e A306803 Can we duplicate a(2) to form a(6)? Yes, as now [a(2) + a(5)] is prime; we get thus a(6) = 1 %e A306803 Can we duplicate a(3) to form a(7)? No, as a(6) + a(3) would be 4 and 4 is not prime; we thus extend S with the smallest integer X not yet in S such that [X + a(6)] is not prime. We get X = 5 and thus a(7) = 5. %e A306803 Can we duplicate a(3) to form a(8)? No, as a(7) + a(3) would be 8 and 8 is not prime; we thus extend S with the smallest integer X not yet in S such that [X + a(7)] is not prime. We get X = 7 and thus a(8) = 7. %e A306803 Can we duplicate a(3) to form a(9)? No, as a(8) + a(3) would be 10 and 10 is not prime; we thus extend S with the smallest integer X not yet in S such that [X + a(8)] is not prime. We get X = 2 and thus a(9) = 2. %e A306803 Can we duplicate a(3) to form a(10)? Yes, as now [a(3) + a(9)] is prime; we get thus a(10) = 3. %e A306803 Can we duplicate a(4) to form a(11)? Yes, as [a(4) + a(10)] is prime; we get thus a(11) = 0. %e A306803 Etc. %Y A306803 Cf. A306808 (which is obtained by replacing prime by palindrome in the definition). %K A306803 base,nonn %O A306803 1,3 %A A306803 _Alexandre Wajnberg_ and _Eric Angelini_, Mar 11 2019