A081023 -id:A081023 - cp's OEIS frontend

A081024 Complement of A081023: actual locations of "t" in this wholly inaccurate variation of the Aronson sentence: "T is the second, third, fifth, sixth, seventh . . . letter of this sentence, not counting commas or spaces".

1, 4, 13, 21, 26, 33, 39, 44, 46, 49, 57, 59, 64, 70, 74, 79, 83, 88, 92, 99, 103, 109, 113, 119, 123, 125, 129, 132, 134, 138, 146, 150, 152, 157, 161, 167, 169, 173, 178, 180, 184, 191, 193, 197, 203, 205, 209, 214, 216, 220, 223, 225, 229, 235, 236, 240, 248

Offset: 1

Matthew Vandermast, Mar 02 2003

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)

Cf. A005224 (Aronson sequence).

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

Original entry on oeis.org

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

N. J. A. Sloane

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

			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...

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).

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.

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

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 *)

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

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

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A081024 Complement of A081023: actual locations of "t" in this wholly inaccurate variation of the Aronson sentence: "T is the second, third, fifth, sixth, seventh . . . letter of this sentence, not counting commas or spaces".

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

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