A005224 T is the first, fourth, eleventh, ... letter in this sentence, not counting spaces or commas (Aronson's sequence). (Formerly M3406)

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

1,2

Comments

a(10^9) = 11281384554. - Hans Havermann, Apr 21 2017

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

Named after the British clinical pharmacologist Jeffrey Kenneth Aronson (b. 1947). - Amiram Eldar, Jun 23 2021

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.

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.

Example

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...

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 *)

Prog

(Python)
from num2words import num2words
from itertools import islice
def n2w(n):
    os = num2words(n, ordinal=True).replace(" and", "")
    return os.replace(" ", "").replace("-", "").replace(", ", "")
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

Crossrefs

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

Sequence in context: A156244 A020961 A336983 * A054870 A197567 A207460

Adjacent sequences: A005221 A005222 A005223 * A005225 A005226 A005227

Keyword

nonn,word,nice

Author

N. J. A. Sloane

Extensions

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

Status

approved