%I M3406 #53 Mar 18 2022 12:29:34

%S 1,4,11,16,24,29,33,35,39,45,47,51,56,58,62,64,69,73,78,80,84,89,94,

%T 99,104,111,116,122,126,131,136,142,147,158,164,169,174,181,183,193,

%U 199,205,208,214,220,226,231,237,243,249,254,270,288,303,307,319,323,341

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

%C a(10^9) = 11281384554. - _Hans Havermann_, Apr 21 2017

%C 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 Named after the British clinical pharmacologist Jeffrey Kenneth Aronson (b. 1947). - _Amiram Eldar_, Jun 23 2021

%D J. K. Aronson, quoted by D. R. Hofstadter in Metamagical Themas, Basic Books, NY, 1985, p. 44.

%D James Gleick, Faster, Vintage Books, NY, 2000 (see pp. 259-261).

%D 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 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Michael S. Branicky, <a href="/A005224/b005224.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 Hans Havermann, <a href="http://gladhoboexpress.blogspot.ca/2017/04/aronsons-sequence.html">Aronson's Sequence</a>.

%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/g4g7.pdf">Seven Staggering Sequences</a>, 2006.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AronsonsSequence.html">Aronson's Sequence</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Aronson%27s_sequence">Aronson's sequence</a>.

%e The sentence begins

%e 1234567890 1234567890 1234567890 1234567890 1234567890

%e Tisthefirs tfourthele venthsixte enthtwenty fourthtwen

%e tyninththi rtythirdth irtyfiftht hirtyninth fortyfifth

%e fortyseven thfiftyfir stfiftysix thfiftyeig hthsixtyse

%e condsixtyf ourthsixty ninthseven tythirdsev entyeighth

%e eightiethe ightyfourt heightynin thninetyfo urthninety

%e ninthonehu ndredfourt honehundre deleventho nehundreds

%e ixteenthon ehundredtw entysecond onehundred twentysixt

%e honehundre dthirtyfir stonehundr edthirtysi xthonehund

%e redfortyse cond...

%t seed="tisthe"; s[1]=1;s[2]=4;

%t name[n_]:=StringReplace[IntegerName[n,{"English","Ordinal"}],{"-"->""," "->""}];

%t s[n_]:=seed=StringJoin[seed<>name[StringPosition[seed,"t"][[n-2,1]]]];

%t l=s/@Range[58]; Table[StringPosition[Last[l],"t"][[i,1]],{i,1,Length[l]}] (* _Ivan N. Ianakiev_, Mar 25 2020 *)

%o (Python)

%o from num2words import num2words

%o from itertools import islice

%o def n2w(n):

%o os = num2words(n, ordinal=True).replace(" and", "")

%o return os.replace(" ", "").replace("-", "").replace(",", "")

%o def agen(): # generator of terms

%o s, idx = "tisthe", 0

%o while True:

%o idx_rel = 1 + s.index("t")

%o idx += idx_rel

%o yield idx

%o s = s[idx_rel:] + n2w(idx)

%o print(list(islice(agen(), 58))) # _Michael S. Branicky_, Mar 18 2022

%Y Cf. A049525, A055508, A081023, A081024, A079000, A097395, A284744.

%K nonn,word,nice

%O 1,2

%A _N. J. A. Sloane_

%E Corrected and extended by Larry Reeves (larryr(AT)acm.org), Oct 31 2000