A005224 T is the first, fourth, eleventh, ... letter in this sentence, not counting spaces or commas (Aronson's sequence).
1, 4, 11, 16, 24, 29, 33, 35, 39, 45, 47, 51, 56, 58, 62, 64, 69, 73, 78, 80, 84, 89, 94, 99, 104, 111, 116, 122, 126, 131, 136, 142, 147, 158, 164, 169, 174, 181, 183, 193, 199, 205, 208, 214, 220, 226, 231, 237, 243, 249, 254, 270, 288, 303, 307, 319, 323, 341
Offset: 1
Examples
The sentence begins 1234567890 1234567890 1234567890 1234567890 1234567890 Tisthefirs tfourthele venthsixte enthtwenty fourthtwen tyninththi rtythirdth irtyfiftht hirtyninth fortyfifth fortyseven thfiftyfir stfiftysix thfiftyeig hthsixtyse condsixtyf ourthsixty ninthseven tythirdsev entyeighth eightiethe ightyfourt heightynin thninetyfo urthninety ninthonehu ndredfourt honehundre deleventho nehundreds ixteenthon ehundredtw entysecond onehundred twentysixt honehundre dthirtyfir stonehundr edthirtysi xthonehund redfortyse cond...
References
- J. K. Aronson, quoted by D. R. Hofstadter in Metamagical Themas, Basic Books, NY, 1985, p. 44.
- James Gleick, Faster, Vintage Books, NY, 2000 (see pp. 259-261).
- 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.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000
- Benoit Cloitre, N. J. A. Sloane and Matthew J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seq., Vol. 6 (2003), Article 03.2.2; arXiv preprint, arXiv:math/0305308 [math.NT], 2003.
- Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See p. 1.
- Hans Havermann, Aronson's Sequence.
- N. J. A. Sloane, Seven Staggering Sequences, 2006.
- Eric Weisstein's World of Mathematics, Aronson's Sequence.
- Wikipedia, Aronson's sequence.
Programs
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Mathematica
seed="tisthe"; s[1]=1;s[2]=4; name[n_]:=StringReplace[IntegerName[n,{"English","Ordinal"}],{"-"->""," "->""}]; s[n_]:=seed=StringJoin[seed<>name[StringPosition[seed,"t"][[n-2,1]]]]; l=s/@Range[58]; Table[StringPosition[Last[l],"t"][[i,1]],{i,1,Length[l]}] (* Ivan N. Ianakiev, Mar 25 2020 *) -
Python
from num2words import num2words from itertools import islice def n2w(n): os = num2words(n, ordinal=True).replace(" and", "") return os.replace(" ", "").replace("-", "").replace(chr(44), "") def agen(): # generator of terms s, idx = "tisthe", 0 while True: idx_rel = 1 + s.index("t") idx += idx_rel yield idx s = s[idx_rel:] + n2w(idx) print(list(islice(agen(), 58))) # Michael S. Branicky, Mar 18 2022
Extensions
Corrected and extended by Larry Reeves (larryr(AT)acm.org), Oct 31 2000
Comments