A070196 -id:A070196 - cp's OEIS frontend

A033899 Sort then Add, a(1)=17.

17, 34, 68, 136, 272, 499, 998, 1897, 3686, 7354, 10811, 11929, 23228, 45466, 90032, 90271, 91550, 93109, 94508, 99097, 107096, 108775, 124553, 248008, 250496, 275065, 300632, 302968, 326657, 562324, 785780, 843568, 1189256, 2314945, 3549404

Offset: 1

N. J. A. Sloane, David W. Wilson

Cf. A033860.

A033899 := proc(n)
    option remember ;
    if n =1 then
        17;
    else
        A070196(procname(n-1)) ;
    end if;
end proc:
seq(A033899(n),n=1..100) ; # R. J. Mathar, Feb 03 2025

NestList[FromDigits[Sort[IntegerDigits[#]]]+#&, 17,40] (* Harvey P. Dale, Apr 07 2018 *)

A033900 Sort then Add, a(1)=19.

Original entry on oeis.org

19, 38, 76, 143, 277, 554, 1009, 1028, 1156, 2312, 3535, 6890, 7579, 13358, 26716, 39383, 72772, 95549, 141148, 252596, 478165, 623843, 857311, 970889, 1049788, 1197677, 2365456, 4711022, 4823269, 7057958, 7615747, 9072524, 9297103, 9420902

Offset: 1

N. J. A. Sloane, David W. Wilson

Cf. A033860.

A033900 := proc(n)
    option remember ;
    if n =1 then
        19;
    else
        A070196(procname(n-1)) ;
    end if;
end proc:
seq(A033900(n),n=1..100) ; # R. J. Mathar, Feb 03 2025

NestList[#+FromDigits[Sort[IntegerDigits[#]]]&,19,40] (* Harvey P. Dale, Sep 02 2022 *)

A033901 Sort then Add, a(1)=21.

Original entry on oeis.org

21, 33, 66, 132, 255, 510, 525, 780, 858, 1446, 2892, 5181, 6339, 9708, 10497, 11976, 23655, 47211, 58458, 104046, 105492, 117951, 229530, 251889, 377778, 755556, 1311123, 2422356, 4645812, 5890380, 5926269, 8182968, 9451857, 10907646

Offset: 1

N. J. A. Sloane, David W. Wilson

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A033860.

A033901 := proc(n)
    option remember ;
    if n =1 then
        21;
    else
        A070196(procname(n-1)) ;
    end if;
end proc:
seq(A033901(n),n=1..100) ; # R. J. Mathar, Feb 03 2025

NestList[FromDigits[Sort[IntegerDigits[#]]]+#&,21,40] (* Harvey P. Dale, Feb 23 2023 *)

a(n)=A033898(n+1), n>1. [From R. J. Mathar, Oct 22 2008]

A033903 Sort then Add, a(1)=27.

Original entry on oeis.org

27, 54, 99, 198, 387, 765, 1332, 2565, 5121, 6246, 8712, 9990, 10989, 12888, 25776, 51453, 64908, 69597, 126396, 250065, 252621, 374877, 722655, 948222, 1170711, 1281888, 2410776, 2535453, 4870008, 4874796, 9342585, 11688174, 22834962

Offset: 1

N. J. A. Sloane, David W. Wilson

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A033860.

A033903 := proc(n)
    option remember ;
    if n =1 then
        27;
    else
        A070196(procname(n-1)) ;
    end if;
end proc:
seq(A033903(n),n=1..100) ; # R. J. Mathar, Feb 03 2025

NestList[#+FromDigits[Sort[IntegerDigits[#]]]&,27,40] (* Harvey P. Dale, May 21 2023 *)

A033904 Sort then Add, a(1)=29.

Original entry on oeis.org

29, 58, 116, 232, 455, 910, 929, 1228, 2456, 4912, 6161, 7327, 9704, 10183, 11321, 22444, 44888, 89776, 157565, 313132, 425465, 670021, 671288, 798076, 865865, 1422553, 2646008, 2670676, 2937353, 5270932, 5494511, 6639070, 6675749

Offset: 1

N. J. A. Sloane, David W. Wilson

Cf. A033860.

A033904 := proc(n)
    option remember ;
    if n =1 then
        29;
    else
        A070196(procname(n-1)) ;
    end if;
end proc:
seq(A033904(n),n=1..100) ; # R. J. Mathar, Feb 03 2025

A033906 Sort then Add, a(1)=20.

Original entry on oeis.org

20, 22, 44, 88, 176, 343, 677, 1354, 2699, 5398, 8987, 16876, 33554, 67009, 67688, 134476, 268943, 503632, 526988, 783877, 1161665, 2277331, 3500708, 3504286, 3738854, 7084642, 7329320, 7552699, 10109498, 10224397, 11447876, 22894654

Offset: 1

N. J. A. Sloane, David W. Wilson

Cf. A033860.

A033906 := proc(n)
    option remember ;
    if n =1 then
        20;
    else
        A070196(procname(n-1)) ;
    end if;
end proc:
seq(A033906(n),n=1..100) ; # R. J. Mathar, Feb 03 2025

NestList[#+FromDigits[Sort[IntegerDigits[#]]]&,20,40] (* Harvey P. Dale, Oct 28 2017 *)

a(n)=A033905(n-1), n>2. [From R. J. Mathar, Oct 22 2008]

A033907 Sort then Add, a(1)=32.

Original entry on oeis.org

32, 55, 110, 121, 233, 466, 932, 1171, 2288, 4576, 9143, 10492, 11741, 22888, 45776, 91453, 104912, 116161, 227327, 449704, 494183, 628672, 855350, 890908, 899807, 978706, 1046495, 1191064, 1302533, 1425868, 2671556, 3927223, 6150602, 6163168

Offset: 1

N. J. A. Sloane, David W. Wilson

Cf. A033860.

A033907 := proc(n)
    option remember ;
    if n =1 then
        32;
    else
        A070196(procname(n-1)) ;
    end if;
end proc:
seq(A033907(n),n=1..100) ; # R. J. Mathar, Feb 03 2025

a(n)=A033902(n+1), n>1. - R. J. Mathar, Oct 22 2008

A371478 Numbers k for which k swaps are needed to bubble-sort the US English number name of k.

Original entry on oeis.org

2, 17, 21, 25

Offset: 1

Eric Angelini and Nicolas Graner, Mar 25 2024

No swaps involve hyphens or spaces.
Only four such numbers < 100 have this property: are there more?
In French, only three such numbers are known: 1, 14, 23.
For number names up to one million, the number of swaps does not exceed 712. - Hans Havermann, Mar 25 2024
There are no more terms. Computationally, there are none < 10^9. If the name of n has k letters, a(n) <= k*(k-1)/2 from the properties of bubble sort.  Also, if 1000^(e-1) <= n < 1000^e, then k <= 41*e, where the loose upper bound comes from "threehundredseventythree" and "quattuordecillion" considering all terms up to 10^66 using English names of large numbers (see Wikipedia link). Thus, a(n) <= 820*e^2 <= 1000^(e-1) for e >= 3. Similar bounds can be derived for extended naming schemes. - Michael S. Branicky, Mar 26 2024

			2 is a term since "two" requires 2 swaps of adjacent letters to sort into ascending alphabetical order: TWO -> TOW -> OTW.

Eric Angelini and Nicolas Graner, More bubble sorting, personal blog, March 2024.
Wikipedia, Names of Large Numbers

Cf. A064038, A070196, A033860.

cp's OEIS Frontend

A033899 Sort then Add, a(1)=17.

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A033900 Sort then Add, a(1)=19.

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A033901 Sort then Add, a(1)=21.

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A033903 Sort then Add, a(1)=27.

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A033904 Sort then Add, a(1)=29.

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A033906 Sort then Add, a(1)=20.

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Maple

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A033907 Sort then Add, a(1)=32.

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Maple

Formula

A371478 Numbers k for which k swaps are needed to bubble-sort the US English number name of k.

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