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 A261310 #12 Aug 16 2015 04:05:52
%S A261310 1,0,29,28,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0,
%T A261310 269,268,267,266,265,264,263,262,261,260,259,258,257,256,255,254,253,
%U A261310 252,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229
%N A261310 a(n+1) = abs(a(n) - gcd(a(n), 10n+9)), a(1) = 1.
%C A261310 The absolute value is relevant only when a(n) = 0 in which case a(n+1) = gcd(a(n),10n+9) = 10n+9.
%C A261310 It is conjectured that for all n, a(n) = 0 implies that a(n+1) = 10n+9 is prime, cf. A186263.
%e A261310 a(2) = a(1) - gcd(a(1),10+9) = 1 - 1 = 0.
%e A261310 a(3) = |a(2) - gcd(a(2),10*2+9)| = gcd(0,29) = 29 is prime.
%e A261310 a(4) = 28 and 10*4+9 = 49, thus a(5) = 28 - gcd(28,49) = 28 - 7 = 21. Note that for n = 4+32, 10n+9 = 329 is divisible by 7, but for n = 5+21 = 26, 10n+9 = 269 = a(27) is prime. Also, for n = 27+269 = 296, 10n+9 = 2969 = a(297) is prime again.
%o A261310 (PARI) print1(a=1);for(n=1,99,print1(",",a=abs(a-gcd(a,10*n+9))))
%Y A261310 Cf. A261301 - A261309; A186253 - A186263.
%K A261310 nonn
%O A261310 1,3
%A A261310 _M. F. Hasler_, Aug 14 2015