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 A332789 #29 Aug 30 2022 02:10:23
%S A332789 1,3,2,2,2,1,3,1,3,2,1,3,1,3,2,2,2,1,3,2,2,2,1,3,1,3,2,2,2,1,3,2,2,2,
%T A332789 1,3,1,3,2,1,3,1,3,2,2,2,1,3,1,3,2,1,3,1,3,2,2,2,1,3,2,2,2,1,3,1,3,2,
%U A332789 1,3,1,3,2,2,2,1,3,1,3,2,1,3,1,3,2,2
%N A332789 First differences of the iterated Beatty sequence A007069.
%C A332789 The sequence A007069 is an iterated Beatty sequence, like the Wythoff compound sequence (A003622(n)) = (A000201(A000201(n))), and the sequence (A140868(n)) = (A003151(A003151(n))). This sequence is the sequence of first differences 1, 3, 2, 2, 2, 1, 3, 1, 3, 2, ... of A007069.
%C A332789 (a(n)) is a morphic sequence, i.e., the letter-to-letter image of the fixed point of a morphism.
%C A332789 Let theta on {a,b,c,d} be the morphism given by
%C A332789 theta : a->adc, b->adc, c->ad, d->bc.
%C A332789 Let the letter-to-letter morphism lambda be given by
%C A332789 lambda : a->1, b->2, c->2, d->3.
%C A332789 Then (a(n)) = lambda(x), where x = adcbcadadc... is the unique fixed point of theta.
%C A332789 See the appendix of my paper "Morphic words, Beatty sequences...".
%H A332789 Michel Dekking, <a href="https://doi.org/10.1016/j.tcs.2019.12.036">Morphic words, Beatty sequences and integer images of the Fibonacci language</a>, Theoretical Computer Science 809, 407-417 (2020).
%F A332789 a(n) = A001951(A001951(n+2)+2) - A001951(A001951(n+1)+1).
%o A332789 (Python)
%o A332789 from math import isqrt
%o A332789 def A332789(n): return isqrt(isqrt(m:=(n+1)**2<<1)**2<<1)-isqrt(isqrt(m-(n<<2)-2)**2<<1) # _Chai Wah Wu_, Aug 29 2022
%Y A332789 Cf. A007069, A001951, A138330.
%Y A332789 Cf. A003622, A000201, A140868, A003151.
%K A332789 nonn
%O A332789 1,2
%A A332789 _Michel Dekking_, Feb 24 2020