A133816 -id:A133816 - cp's OEIS frontend

A131744 Eric Angelini's "1995" puzzle: the sequence is defined by the property that if one writes the English names for the entries, replaces each letter with its rank in the alphabet and calculates the absolute values of the differences, one recovers the sequence.

1, 9, 9, 5, 5, 9, 9, 5, 5, 9, 1, 3, 13, 17, 1, 3, 13, 17, 9, 5, 5, 9, 9, 5, 5, 9, 1, 3, 13, 17, 1, 3, 13, 17, 9, 5, 5, 9, 10, 1, 9, 15, 12, 10, 13, 0, 15, 12, 1, 9, 2, 15, 0, 9, 5, 14, 17, 17, 9, 6, 15, 0, 9, 1, 1, 9, 15, 12, 10, 13, 0, 15, 12, 1, 9, 2, 15, 0, 9, 5, 14, 17, 17, 9

Offset: 1

Eric Angelini, Sep 20 2007

In the first few million terms, the numbers 16, 19, 20 and 22-26 do not occur. Of the numbers that do occur, the number 11 appears with the smallest frequence - see A133152. - N. J. A. Sloane, Sep 22 2007
From David Applegate, Sep 24 2007: (Start)
The numbers 16, 19-20, 22-25 never occur in the sequence. The following table gives the possible numbers that can occur in the sequence and for each one, the possible numbers that can follow it. The table is complete - when any number and its successor are expanded, the resulting pairs are also in the table. It contains the expansion of 1 and thus describes all possible transitions:
-> 0,1,4,5,7,9,10,12,15,21
-> 1,3,5,9,12
-> 1,3,12,15
-> 0,1,2,3,4,5,8,9,11,12,13,14,18
-> 2,3,12,14
-> 3,5,9,10,12,14,15
-> 3,5,12,15,21
-> 7,10,17
-> 0,3,5,9
-> 0,1,2,3,4,5,6,8,9,10,12,14,15,21
-> 1,13,15,17
-> 21
-> 0,1,6,9,10,14,15,21
-> 0,3,17
-> 3,10,15,17
-> 0,3,4,9,12,15,18
-> 1,9,10,14,15,17,21
-> 3,7,9
-> 13,21
(End)
The sequence may also be extended in the reverse direction: ... 0 21 21 13 3 0 [then what we have now] 1 9 9 5 5 ..., corresponding to ... zero twentyone twentyone thirteen three zero one nine nine five ... - N. J. A. Sloane, Sep 27 2007
The name of this sequence ("Eric Angelini's ... puzzle") was added by N. J. A. Sloane many months after Eric Angelini submitted it.
Begin with 1, map the integer to its name and then map according to A073029, compute the absolute difference, spell out that difference; iterate as necessary. - Robert G. Wilson v, Jun 08 2010

			O.N.E...N.I.N.E...N.I.N.E...F.I..V..E...F.I..V..E...
.1.9..9..5.5.9..9..5.5.9..1..3.13.17..1..3.13.17....
1 -> "one" -> 15,14,5 -> (the difference is) 1,9; iterate. Therefore 1,9 -> "one,nine"; -> 15,14,5,14,9,14,5 -> 1,9,9,5,5,9; "one,nine,nine,five,five,nine"; etc. - _Robert G. Wilson v_, Jun 08 2010

N. J. A. Sloane, Table of n, a(n) for n = 1..40000
N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 9.

Cf. A131745, A131746, A130316, A133152, A133816, A133817.

Cf. A131285 (ranks of letters), A131286, A131287.

Nest[Abs@Differences@Flatten[LetterNumber[Characters[IntegerName@#]/."-"->""]&/@#]&,{1},4] (* Giorgos Kalogeropoulos, Apr 11 2021 *)

def chrdist(a, b): return abs(ord(a)-ord(b))
def aupto(nn):
  allnames = "zero,one,two,three,four,five,six,seven,eight,nine,ten,eleven,twelve,thirteen,fourteen,fifteen,sixteen,seventeen,eighteen,nineteen,twenty,twentyone"
  names = allnames.split(",")
  alst, aidx, last, nxt = [1, 9], 1, "e", "one"
  while len(alst) < nn:
    nxt = names[alst[aidx]]
    alst += [chrdist(a, b) for a, b in zip(last+nxt[:-1], nxt)]
    last, aidx = nxt[-1], aidx + 1
  return alst[:nn]
print(aupto(84)) # Michael S. Branicky, Jan 09 2021

More terms from N. J. A. Sloane, Sep 20 2007

A131745 First French version of A131744.

Original entry on oeis.org

4, 20, 19, 2, 13, 17, 13, 5, 7, 13, 16, 5, 15, 10, 9, 16, 15, 2, 1, 16, 3, 4, 2, 13, 4, 17, 21, 1, 5, 15, 5, 14, 11, 4, 0, 2, 13, 4, 17, 21, 2, 6, 5, 3, 2, 14, 11, 4, 0, 2, 13, 4, 17, 21, 14, 14, 4, 17, 21, 2, 6, 5, 3, 0, 4, 12, 5, 12, 21, 1, 5, 15, 10, 9, 16, 15, 13, 14, 4, 17

Offset: 1

Michael Kleber, Sep 20 2007

Diacritics are ignored when computing the rank of a letter.
Spellings used for French numbers: zero, un, deux, trois, quatre, cinq, six, sept, huit, neuf, dix, onze, douze, treize, quatorze, quinze, seize, dix-sept, dix-huit, dix-neuf, vingt, vingt et un, vingt-deux, vingt-trois, vingt-quatre, vingt-cinq.
The numbers 18 and 22-25 do not occur in the sequence. - David Applegate, Sep 24 2007
There appears to be no analog in Spanish. (The requirement is that the difference between the ranks of the first two letters in the word for the number n should equal n.) - David Applegate, Sep 24 2007. There exists such a sequence (namely, 12, 13, 2, 16, 2, 14, 2, 2, 1...) if (as is standard) letter 'ñ' is granted an alphabet position, whereas digraphs such as 'll' are not. - Álvar Ibeas, Sep 18 2020

			The sequence begins Quatre, vingt, dix-neuf, deux, treize, ...

Cf. A131744, A131746, A130316, A133816, A133817.

More terms from David Applegate, Sep 24 2007

A131746 Second French version of A131744.

Original entry on oeis.org

9, 16, 15, 13, 14, 4, 17, 21, 12, 4, 12, 5, 12, 21, 15, 2, 13, 4, 17, 21, 12, 4, 20, 19, 5, 3, 8, 21, 12, 4, 20, 19, 2, 13, 1, 5, 15, 5, 14, 11, 4, 2, 13, 5, 7, 13, 15, 15, 1, 7, 10, 11, 6, 5, 21, 12, 4, 20, 19, 2, 13, 1, 11, 6, 5, 21, 2, 6, 5, 3, 13, 11, 6, 5, 21, 17, 13, 5, 7

Offset: 1

Michael Kleber, Sep 20 2007

Diacritics are ignored when computing the rank of a letter.

The numbers 18 and 22-25 do not occur in the sequence. - David Applegate, Sep 24 2007

			The sequence begins Neuf, seize, quinze, treize, quatorze, ...

Cf. A131744, A131745, A130316, A133816, A133817.

More terms from David Applegate, Sep 24 2007

A133817 Second German version of A131744.

Original entry on oeis.org

15, 7, 8, 20, 21, 3, 6, 5, 10, 4, 3, 3, 9, 13, 2, 5, 12, 6, 3, 22, 13, 12, 17, 2, 2, 4, 5, 7, 7, 10, 22, 3, 22, 13, 12, 17, 2, 3, 14, 13, 4, 10, 14, 2, 5, 11, 13, 15, 7, 8, 20, 21, 3, 6, 8, 13, 4, 13

Offset: 1

David Applegate, Sep 24 2007

Diacritics are ignored when computing the rank of a letter.

The numbers 23 and 25 do not occur in the sequence.

			The sequence begins Funfzehn, sieben, acht, zwanzig, einundzwanzig, drei, ...

Cf. A131744, A131745, A131746, A130716, A133816.

A130316 Italian version of A131744.

Original entry on oeis.org

4, 20, 19, 0, 2, 3, 7, 17, 9, 6, 11, 5, 5, 6, 6, 8, 13, 0, 1, 7, 17, 21, 21, 13, 3, 11, 17, 16, 15, 2, 13, 14, 14, 15, 0, 15, 1, 5, 6, 6, 8, 18, 0, 14, 15, 0, 15, 9, 1, 7, 17, 14, 14, 4, 12, 7, 10, 5, 6, 6, 6, 6, 5, 3, 4, 16, 2, 6, 5, 3, 4, 16, 14, 14, 4, 10, 14, 4, 6, 5, 0, 5, 5, 2, 13

Offset: 1

N. J. A. Sloane, Sep 21 2007

Spellings used for Italian numbers: zero, un, due, tre, quattro, cinque, sei, sette, otto, nove, dieci, undici, dodici, tredici, quattordici, quindici, sedici, diciassette, diciotto, diciannove, venti, ventuno, ventidue, ventitre, ventiquattro, venticinque.

The numbers 22-25 do not occur in the sequence. - David Applegate, Sep 24 2007

			The sequence begins Quattro, venti, diciannove, zero, due, tre, sette, ...

Cf. A131744, A131745, A131746, A133816, A133817.

More terms from David Applegate, Sep 24 2007

cp's OEIS Frontend

A131744 Eric Angelini's "1995" puzzle: the sequence is defined by the property that if one writes the English names for the entries, replaces each letter with its rank in the alphabet and calculates the absolute values of the differences, one recovers the sequence.

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A131745 First French version of A131744.

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A131746 Second French version of A131744.

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A133817 Second German version of A131744.

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A130316 Italian version of A131744.

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