A060403 -id:A060403 - cp's OEIS frontend

A375119 Begin A060403 with n instead of 1; a(n) is the position in the new sequence at which it generates the same numbers as A060403 or a(n)=0 if it doesn't.

1, 4, 2, 1, 3, 3, 6, 1, 2, 2, 5, 5, 1, 5, 5, 6, 4, 4, 10, 4, 1, 4, 5, 5, 3, 3, 9, 9, 9, 1, 3, 9, 4, 4, 2, 1, 8, 8, 8, 2, 8, 5, 3, 3, 1, 2, 27, 7, 7, 4, 7, 5, 2, 1, 3, 3, 26, 6, 6, 4, 6, 26, 1, 2, 3, 3, 25, 5, 5, 25, 5, 25, 1, 2, 3, 3, 24, 4, 4, 3, 4, 24, 113

Offset: 1

James C. McMahon, Jul 30 2024

The indices of the matching entries of A060403 and this sequence do not necessarily have to be the same (see Examples).

			Using () to indicate the point at which the new sequence generates the same numbers as A060403:
  A060403: 1, 4, 8, 13, 21, 30, 36, 45...      a(1)=1
  Start=2: 2, 6, 9, (13), 21, 30, 36, 45...    a(2)=4
  Start=3: 3, (8), 13, 21, 30, 36, 45...       a(3)=2
  Start=4: (4), 8, 13, 21, 30, 36, 45...       a(4)=1

James C. McMahon, Table of n, a(n) for n = 1..1000
Wikipedia,Kruskal count

Cf. A060403.

oneseq=NestList[#+Length[Select[Characters[IntegerName[#,"Words"]],LetterQ ]]&,1,200] (* oneseq is A060403 *);seq={};Do[ i=1;s=n;While[!MemberQ[oneseq,s],s=s+Length[Select[Characters[IntegerName[s,"Words"]],LetterQ ]];i++];AppendTo[seq,i],{n,83}];seq

A192740 Spanish version of A060403 - Each term is the previous term plus the number of letters in the previous number, as conventionally spelled out in Spanish.

Original entry on oeis.org

1, 3, 7, 12, 16, 25, 36, 48, 61, 72, 83, 95, 108, 118, 133, 151, 170, 183, 201, 214, 231, 252, 275, 298, 320, 337, 361, 383, 406, 423, 446, 472, 496, 521, 540, 558, 582, 603, 618, 638, 661, 683, 706, 721, 741, 764, 789, 813, 829, 851, 875, 899, 923, 944, 970

Offset: 1

Claudio Meller, Jul 09 2011

The sequence of words is: uno, tres, siete, doce, dieciseis, veinticinco, treinta y seis, ...

			a(5)= number of letters of uno-tres-siete-doce = 16.

A139097 Form a sequence of words as follows: look to the left, towards the beginning of the sequence and write down the number of letters you see; repeat; then replace the words with the corresponding numbers.

Original entry on oeis.org

0, 4, 8, 13, 21, 30, 36, 45, 54, 63, 73, 85, 95, 105, 119, 137, 158, 178, 200, 211, 227, 248, 268, 288, 309, 325, 347, 369, 390, 408, 424, 445, 465, 485, 506, 520, 537, 559, 579, 601, 614, 632, 651, 669, 688, 709, 725, 747, 769, 790, 808, 825, 847, 869, 890, 908, 924, 945, 965, 985, 1006, 1020, 1037, 1059

Offset: 0

Jonathan Vos Post, May 12 2007

The sequence of words is: zero, four, eight, thirteen, twenty-one, thirty, ... (in American English).
Hyphens and spaces are not counted.
This is an English version of the sequence in A139121.
a(0) = 0, a(n+1) = a(n) + A005589(a(n)). - Jonathan Vos Post, Jun 15 2008

			The second word is "four" (and so a(2)=4), because at the end of the first word we can see four letters to the left.

E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.

M. F. Hasler, Table of n, a(n) for n = 0..423

Cf. A005589. See A060403 and A139121 for other versions.

Edited by N. J. A. Sloane, Jun 08 2008

More terms from M. F. Hasler and R. J. Mathar, Jun 15 2008

A139121 Total number of letters in the preceding terms spelled out in French.

Original entry on oeis.org

0, 4, 10, 13, 19, 26, 34, 46, 57, 70, 81, 94, 113, 123, 137, 151, 168, 184, 205, 217, 232, 250, 267, 287, 310, 322, 340, 357, 379, 403, 418, 435, 455, 478, 503, 516, 529, 546, 565, 585, 608, 619, 633, 651, 671, 692, 715, 729, 746, 765, 785, 808, 820, 833, 852, 873, 895, 920, 933, 952, 973, 995, 1020

Offset: 1

N. J. A. Sloane (based on Angelini's article), Jun 08 2008, Jun 15 2008

Form a sequence of French words as follows: look to the left, towards the beginning of the sequence and write down the number of letters you see; repeat; then replace the words by the corresponding numbers.
The sequence of words is: zero, quatre, dix, treize, dix-neuf, vingt-six, trente-quatre, quarante-six, cinquante-sept, ...
Hyphens, accents and spaces are not counted.
For an English version see A139097.

			The first word is "zero", because initially there are no letters to the left. The second word is "quatre" (and so a(2)=4), because at the end of the first word we can see four letters to the left. And so on.

E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.

Cf. A005589, A060403, A139097.

A139121(n)={ n>1 & return( #select(Vec(French(n=A139121(n-1))),x->x>"@")+n )}  /* see A167507 for French() */  \\ M. F. Hasler, Sep 29 2011

Offset and a(9) corrected (according to wording of example) and terms beyond a(9) from M. F. Hasler, Sep 29 2011

A160395 Each term is the previous term plus the number of letters in the previous number, as conventionally spelled out in British English.

Original entry on oeis.org

1, 4, 8, 13, 21, 30, 36, 45, 54, 63, 73, 85, 95, 105, 122, 144, 166, 187, 211, 230, 249, 271, 294, 317, 341, 364, 388, 414, 436, 459, 482, 505, 523, 548, 572, 596, 619, 640, 658, 681, 703, 723, 749, 773, 800, 812, 833, 859, 883, 909, 927, 952, 974, 999, 1023

Offset: 1

Carl R. White, May 12 2009

Increases a little faster than A060403 since British English uses 'and' to separate hundreds from the rest of the number. e.g. 619 = "six hundred and nineteen" in British English but "six hundred nineteen" in American English

GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See pages 49 and 214.

For American English see A060403

A094110 Start with the word "One". The next word is the number of letters written previously. Convert this infinite sequence of words into an infinite sequence of numbers.

Original entry on oeis.org

1, 3, 8, 13, 21, 30, 36, 45, 54, 63, 73, 85, 95, 105, 119, 137, 158, 178, 200, 210, 223, 244, 263, 283, 304, 320, 338, 361, 381, 402, 416, 434, 455, 475, 497, 519, 538, 560, 576, 597, 619, 637, 658, 678, 700, 712, 730, 748, 770, 789, 811, 829, 851, 871, 893

Offset: 1

Eric Angelini, May 03 2004

Variant of A060403. [From R. J. Mathar, Dec 15 2008]

			The sentence begins
1234567890 1234567890 1234567890 1234567890 1234567890
OneThreeEi ghtThirtee nTwentyone ThirtyThir tysixForty
fiveFiftyf ourSixtyth reeSeventy threeEight yfiveNinet
yfiveOnehu ndredfiveO nehundredn ineteenOne hundredthi
rtysevenOn ehundredfi ftyeightOn ehundredse ventyeight
Twohundred Twohundred tenTwohund redtwentyt hreeTwohun
dredfortyf ourTwohund redsixtyth reeTwohund redeightyt
hreeThreeh undredfour Threehundr edtwentyTh reehundred
thirtyeigh tThreehund redsixtyon eThreehund redeightyo
neFourhund redtwoFour hundredsix teenFourhu ndredthirt
yfourFourh undredfift yfiveFourh undredseve ntyfiveFou
rhundredni netysevenF ivehundred nineteenFi vehundredt
hirtyeight Fivehundre dsixtyFive hundredsev entysixFiv
ehundredni netysevenS ixhundredn ineteenSix hundredthi
rtysevenSi xhundredfi ftyeightSi xhundredse ventyeight
Sevenhundr edSevenhun dredtwelve Sevenhundr edthirtySe
venhundred fortyeight Sevenhundr edseventyS evenhundre
deightynin eEighthund redelevenE ighthundre dtwentynin
eEighthund redfiftyon eEighthund redseventy oneEighthu
ndredninet ythreeNine hundredsix teenNinehu ndredthirt

Landon Curt Noll, The English name of a number.

Cf. A005224, A049525 & A055508.

Edited and extended by Robert G. Wilson v, May 14 2004

A129731 Each term is the previous term times the number of letters in the previous number, as conventionally spelled out in English.

Original entry on oeis.org

1, 3, 15, 105, 1470, 42630, 1364160, 75028800, 3676411200, 272054428800

Offset: 1

Jonathan Vos Post, May 12 2007, May 22 2007

Multiplicative analog of A060403.

			a(1) = 1.
a(2) = 1 * A060403(1) = 1 * LettersIn("one") = 1*3 = 3.
a(3) = 3 * A060403(2) = 3 * LettersIn("three") = 3*5 = 15.
a(4) = 15 * A060403(3) = 15 * LettersIn("fifteen") = 15*7 = 105.
a(10) = 74 * A060403(a(9)) = 74 * LettersIn("three billion six hundred seventysix million four hundred eleven thousand two hundred") = 1364160 * 55 * 49 * 74 = 272054 28800 = 2^7 * 3 * 5^2 * 7^4 * 11 * 29 * 37.

Cf. A005589, A060403.

a(0) = 1; a(n+1) = a(n) * A005589(a(n)). a(0) = 1; a(n+1) = PRODUCT[i=1..n] A005589(a(i)).

A161366 Each term is the previous term plus the number of letters in the previous number, as conventionally spelled out in Spanish.

Original entry on oeis.org

1, 4, 10, 14, 21, 30, 37, 50, 59, 74, 88, 100, 104, 116, 131, 148, 167, 186, 204, 220, 236, 258, 282, 303, 318, 338, 361, 383, 406, 423, 446, 472, 496, 521, 540, 558, 582, 603, 618, 638, 661, 683, 706, 721, 741, 764, 789, 813, 829, 851, 875, 899, 923, 944, 970

Offset: 1

Claudio Meller, Jun 07 2009

1= uno(3 letters), 1+3 = 4 = cuatro (6 letters) 4+6=10, etc

Cf. A060403.

cp's OEIS Frontend

A375119 Begin A060403 with n instead of 1; a(n) is the position in the new sequence at which it generates the same numbers as A060403 or a(n)=0 if it doesn't.

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A192740 Spanish version of A060403 - Each term is the previous term plus the number of letters in the previous number, as conventionally spelled out in Spanish.

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A139097 Form a sequence of words as follows: look to the left, towards the beginning of the sequence and write down the number of letters you see; repeat; then replace the words with the corresponding numbers.

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A139121 Total number of letters in the preceding terms spelled out in French.

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A160395 Each term is the previous term plus the number of letters in the previous number, as conventionally spelled out in British English.

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A094110 Start with the word "One". The next word is the number of letters written previously. Convert this infinite sequence of words into an infinite sequence of numbers.

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A129731 Each term is the previous term times the number of letters in the previous number, as conventionally spelled out in English.

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A161366 Each term is the previous term plus the number of letters in the previous number, as conventionally spelled out in Spanish.

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