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 A001544 M4346 N1820 #39 Jan 15 2025 14:06:35
%S A001544 1,7,13,97,8833,77968897,6079148431583233,
%T A001544 36956045653220845240164417232897,
%U A001544 1365749310322943329964576677590044473746108255675592519835615233
%N A001544 A nonlinear recurrence: a(n) = a(n-1)^2 - 6*a(n-1) + 6, with a(0) = 1, a(1) = 7.
%C A001544 This is the special case k=6 of sequences with exact mutual k-residues. In general, a(1)=k+1 and a(n)=min{m | m>a(n-1), mod(m,a(i))=k, i=1,...,n-1}. k=1 gives Sylvester's sequence A000058 and k=2 Fermat sequence A000215. - _Seppo Mustonen_, Sep 04 2005
%D A001544 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001544 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001544 Indranil Ghosh, <a href="/A001544/b001544.txt">Table of n, a(n) for n = 0..11</a>
%H A001544 S. W. Golomb, <a href="http://www.jstor.org/stable/2311857">On certain nonlinear recurring sequences</a>, Amer. Math. Monthly 70 (1963), 403-405.
%H A001544 R. Mestrovic, <a href="http://arxiv.org/abs/1202.3670">Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof</a>, arXiv preprint arXiv:1202.3670 [math.HO], 2012. - _N. J. A. Sloane_, Jun 13 2012
%H A001544 Seppo Mustonen, <a href="http://www.survo.fi/papers/resseq.pdf">On integer sequences with mutual k-residues</a>
%H A001544 Seppo Mustonen, <a href="/A000215/a000215.pdf">On integer sequences with mutual k-residues</a> [Local copy]
%H A001544 <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F A001544 a(n) ~ c^(2^n), where c = 1.76450357631319101484804524709844019487003729926754942591419313922841785792... . - _Vaclav Kotesovec_, Dec 17 2014
%t A001544 Flatten[{1,RecurrenceTable[{a[1]==7, a[n]==a[n-1]*(a[n-1]-6)+6}, a, {n, 1, 10}]}] (* _Vaclav Kotesovec_, Dec 17 2014 *)
%t A001544 Join[{1},NestList[#^2-6#+6&,7,10]] (* _Harvey P. Dale_, Nov 19 2024 *)
%o A001544 (PARI) a(n)=if(n<1, n==0, if(n==1, 7, n=a(n-1); n^2-6*n+6))
%Y A001544 Column k=6 of A177888. - _Alois P. Heinz_, Nov 07 2012
%K A001544 nonn
%O A001544 0,2
%A A001544 _N. J. A. Sloane_