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A005224 T is the first, fourth, eleventh, ... letter in this sentence, not counting spaces or commas (Aronson's sequence).

%I A005224 M3406 #61 Jul 30 2025 11:21:01
%S A005224 1,4,11,16,24,29,33,35,39,45,47,51,56,58,62,64,69,73,78,80,84,89,94,
%T A005224 99,104,111,116,122,126,131,136,142,147,158,164,169,174,181,183,193,
%U A005224 199,205,208,214,220,226,231,237,243,249,254,270,288,303,307,319,323,341
%N A005224 T is the first, fourth, eleventh, ... letter in this sentence, not counting spaces or commas (Aronson's sequence).
%C A005224 a(10^9) = 11281384554. - _Hans Havermann_, Apr 21 2017
%C A005224 First differences start: 3, 7, 5, 8, 5, 4, 2, 4, 6, 2, 4, 5, 2, 4, 2, 5, 4, 5, 2, 4, 5, 5, 5, 5, 7, 5, 6, 4, 5, 5, 6, 5, 11, 6, 5, 5, 7, 2, 10, 6, ... - _Daniel Forgues_, Sep 11 2019
%C A005224 Named after the British clinical pharmacologist Jeffrey Kenneth Aronson (b. 1947). - _Amiram Eldar_, Jun 23 2021
%D A005224 J. K. Aronson, quoted by D. R. Hofstadter in Metamagical Themas, Basic Books, NY, 1985, p. 44.
%D A005224 James Gleick, Faster, Vintage Books, NY, 2000 (see pp. 259-261).
%D A005224 N. J. A. Sloane, Seven Staggering Sequences, in Homage to a Pied Puzzler, E. Pegg Jr., A. H. Schoen and T. Rodgers (editors), A. K. Peters, Wellesley, MA, 2009, pp. 93-110.
%D A005224 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005224 Michael S. Branicky, <a href="/A005224/b005224.txt">Table of n, a(n) for n = 1..10000</a>
%H A005224 Benoit Cloitre, N. J. A. Sloane and Matthew J. Vandermast, <a href="http://www.emis.de/journals/JIS/VOL6/Cloitre/cloitre2.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seq., Vol. 6 (2003), Article 03.2.2; <a href="https://arxiv.org/abs/math/0305308">arXiv preprint</a>, arXiv:math/0305308 [math.NT], 2003.
%H A005224 Robbert Fokkink and Gandhar Joshi, <a href="https://arxiv.org/abs/2507.16956">On Cloitre's hiccup sequences</a>, arXiv:2507.16956 [math.CO], 2025. See p. 1.
%H A005224 Hans Havermann, <a href="http://gladhoboexpress.blogspot.ca/2017/04/aronsons-sequence.html">Aronson's Sequence</a>.
%H A005224 N. J. A. Sloane, <a href="http://neilsloane.com/doc/g4g7.pdf">Seven Staggering Sequences</a>, 2006.
%H A005224 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AronsonsSequence.html">Aronson's Sequence</a>.
%H A005224 Wikipedia, <a href="https://en.wikipedia.org/wiki/Aronson%27s_sequence">Aronson's sequence</a>.
%e A005224 The sentence begins
%e A005224 1234567890 1234567890 1234567890 1234567890 1234567890
%e A005224 Tisthefirs tfourthele venthsixte enthtwenty fourthtwen
%e A005224 tyninththi rtythirdth irtyfiftht hirtyninth fortyfifth
%e A005224 fortyseven thfiftyfir stfiftysix thfiftyeig hthsixtyse
%e A005224 condsixtyf ourthsixty ninthseven tythirdsev entyeighth
%e A005224 eightiethe ightyfourt heightynin thninetyfo urthninety
%e A005224 ninthonehu ndredfourt honehundre deleventho nehundreds
%e A005224 ixteenthon ehundredtw entysecond onehundred twentysixt
%e A005224 honehundre dthirtyfir stonehundr edthirtysi xthonehund
%e A005224 redfortyse cond...
%t A005224 seed="tisthe"; s[1]=1;s[2]=4;
%t A005224 name[n_]:=StringReplace[IntegerName[n,{"English","Ordinal"}],{"-"->""," "->""}];
%t A005224 s[n_]:=seed=StringJoin[seed<>name[StringPosition[seed,"t"][[n-2,1]]]];
%t A005224 l=s/@Range[58]; Table[StringPosition[Last[l],"t"][[i,1]],{i,1,Length[l]}] (* _Ivan N. Ianakiev_, Mar 25 2020 *)
%o A005224 (Python)
%o A005224 from num2words import num2words
%o A005224 from itertools import islice
%o A005224 def n2w(n):
%o A005224     os = num2words(n, ordinal=True).replace(" and", "")
%o A005224     return os.replace(" ", "").replace("-", "").replace(chr(44), "")
%o A005224 def agen(): # generator of terms
%o A005224     s, idx = "tisthe", 0
%o A005224     while True:
%o A005224         idx_rel = 1 + s.index("t")
%o A005224         idx += idx_rel
%o A005224         yield idx
%o A005224         s = s[idx_rel:] + n2w(idx)
%o A005224 print(list(islice(agen(), 58))) # _Michael S. Branicky_, Mar 18 2022
%Y A005224 Cf. A049525, A055508, A081023, A081024, A079000, A097395, A284744.
%K A005224 nonn,word,nice
%O A005224 1,2
%A A005224 _N. J. A. Sloane_
%E A005224 Corrected and extended by Larry Reeves (larryr(AT)acm.org), Oct 31 2000