A005589 -id:A005589 - cp's OEIS frontend

A067278 a(n) = letters(n) + a(n-1); a(0) = 0.

0, 3, 6, 11, 15, 19, 22, 27, 32, 36, 39, 45, 51, 59, 67, 74, 81, 90, 98, 106, 112, 121, 130, 141, 151, 161, 170, 181, 192, 202, 208, 217, 226, 237, 247, 257, 266, 277, 288, 298, 303, 311, 319, 329, 338, 347, 355, 365, 375, 384, 389, 397, 405, 415, 424, 433, 441

Offset: 0

Scott A. Brown, Feb 22 2002

			0 + one = 3, 3 + two = 6, 6 + three = 11, 11 + four = 15, 15 + five = 19, ....

Cf. A005589, A052360, A052362, A052363.

a(n) = A005589(n) + a(n-1). - Michael S. Branicky, Mar 03 2025

A163828 Number of straight line segments in all letters of the capitalized English name of n.

Original entry on oeis.org

9, 7, 6, 15, 5, 10, 3, 13, 12, 11, 9, 19, 18, 21, 18, 20, 16, 26, 23, 24, 18, 25, 24, 33, 23, 28, 21, 31, 30, 29, 13, 20, 19, 28, 18, 23, 16, 26, 25, 24, 10, 17, 16, 25, 15, 20, 13, 23, 22, 21, 12, 19, 18, 27, 17, 22, 15, 25, 24, 23, 8, 15, 14, 23, 13, 18, 11, 21, 20, 19, 18

Offset: 0

Jonathan Vos Post, Aug 05 2009

Number of straight line segments (chisel strokes) in the capitalized English name of n (excluding spaces and hyphens), counting smooth curves as zero strokes.
The 15 letters which are entirely strokes (no curves): A(3), E(4), F(3), H(3), I(1), K(3), L(2), M(4), N(3), T(2), V(2), W(4), X(2), Y(3), Z(3).
Those 4 which are entirely curves (and count as zero): C, O, S, U.
Those 7 which mix strokes and curves: B(1), D(1), G(2), J(1), P(1), Q(1), R(2).
a(16)=16 is a fixed point.
The numbers written entirely from stroke-only letters are A163670.

			a(0) = 9 because ZERO has (letter by letter) 3+4+2+0 = 9 straight line segments (chisel strokes).
a(1) = 7 because ONE has 0+3+4 = 7 strokes.
a(20) = 18 because TWENTY (all strokes) has 2+4+4+3+2+3 = 18 strokes.

Cf. A002963, A005589, A163670.

names :=["zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine",
"ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen",
"nineteen", "twenty", "twentyone", "twentytwo", "twentythree", "twentyfour", "twentyfive", "twentysix",
"twentyseven", "twentyeight", "twentynine", "thirty", "thirtyone", "thirtytwo", "thirtythree",
"thirtyfour", "thirtyfive", "thirtysix", "thirtyseven", "thirtyeight", "thirtynine", "forty",
"fortyone", "fortytwo", "fortythree", "fortyfour", "fortyfive", "fortysix", "fortyseven",
"fortyeight", "fortynine", "fifty", "fiftyone", "fiftytwo", "fiftythree", "fiftyfour",
"fiftyfive", "fiftysix", "fiftyseven", "fiftyeight", "fiftynine", "sixty", "sixtyone",
"sixtytwo", "sixtythree", "sixtyfour", "sixtyfive", "sixtysix", "sixtyseven", "sixtyeight",
"sixtynine", "seventy", "seventyone", "seventytwo", "seventythree", "seventyfour",
"seventyfive", "seventysix", "seventyseven", "seventyeight", "seventynine", "eighty",
"eightyone", "eightytwo", "eightythree", "eightyfour", "eightyfive", "eightysix",
"eightyseven", "eightyeight", "eightynine", "ninety", "ninetyone", "ninetytwo",
"ninetythree", "ninetyfour", "ninetyfive", "ninetysix", "ninetyseven", "ninetyeight",
"ninetynine", "onehundred"] :
cstrok := [ 3, 1, 0, 1, 4, 3, 2, 3, 1, 1, 3, 2, 4, 3, 0, 1, 1, 2, 0, 2, 0, 2, 4, 2, 3, 3 ] ;
A163828 := proc(n) global names, cstrok; a := 0 ; for c in StringTools[Explode]( names[n+1]) do a := a+ cstrok[StringTools[Ord](c)-96] ; od: a ; end:
seq(A163828(n),n=0..70) ; # R. J. Mathar, Sep 29 2009

a(36) changed to 16 by R. J. Mathar, Sep 29 2009

A233184 a(n) is the least number larger than the total number of letters in the English names for all terms up to and including a(n).

Original entry on oeis.org

5, 9, 16, 26, 35, 40, 49, 59, 66, 76, 86, 95, 109, 129, 149, 166, 186, 200, 209, 229, 249, 266, 286, 300, 316, 339, 359, 380, 399, 418, 439, 459, 480, 496, 510, 530, 546, 566, 586, 600, 609, 629, 649, 666, 686, 700, 716, 739, 759, 780, 799, 819, 840, 856, 879, 900, 905, 926, 945, 965, 986, 1000, 1010, 1030, 1046, 1066, 1086, 1110

Offset: 1

Eric Angelini and M. F. Hasler, Dec 05 2013

See A233185-A233188 for French and German variants.

E. Angelini, Cumulative quantity of letters used in a list of English number-names, SeqFan list, Dec 05 2013

a=0;k=0;for(n=1,99,until( k++ > a + A005589(k),); print1(k,","); a+=A005589(k))

A107322 English name for number and its reverse have the same number of letters.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 22, 33, 34, 35, 38, 41, 43, 44, 45, 48, 53, 54, 55, 58, 66, 67, 69, 76, 77, 79, 83, 84, 85, 88, 96, 97, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 112, 113, 115, 118, 121, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132

Offset: 0

David W. Wilson, May 21 2005

Obviously includes all palindromes (A002113).

			35 is in sequence because 35 ("thirty-five") and 53 ("fifty-three") each have 10 letters in English (dashes not counted).

Michael S. Branicky, Table of n, a(n) for n = 0..10000

Cf. A002113, A004086, A005589.

Select[Range[0,132],Length[Select[Characters[IntegerName[#,"Words"]],LetterQ]]==Length[Select[Characters[IntegerName[FromDigits[Reverse[IntegerDigits[#]]],"Words"]],LetterQ]]&] (* James C. McMahon, Feb 12 2024 *)

from num2words import num2words
def n2w(n):
  map = {ord(c): None for c in "-, "}
  return num2words(n).replace(" and", "").translate(map)
def ok(n): return len(n2w(n)) == len(n2w(int(str(n)[::-1])))
print([k for k in range(133) if ok(k)]) # Michael S. Branicky, Feb 12 2024

10 inserted by James C. McMahon, Feb 12 2024

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

A163670 Numbers whose English name (excluding spaces and hyphens) is written with only straight line segments (chisel strokes).

Original entry on oeis.org

5, 9, 10, 11, 12, 15, 19, 20, 25, 29, 50, 55, 59, 90, 95, 99

Offset: 1

Jonathan Vos Post, Aug 02 2009

There are no elements in the sequence beyond 99 because of curves in writing hUnDReD, thOUSanD, milliOn, BilliOn, and so forth. If one counts the segments (chisel strokes) then 29 is the unique fixed point of that derived sequence.

Specifically, these are the numbers whose names use only the letters A, E, F, H, I, K, L, M, N, T, V, W, X, Y, and Z. [From Franklin T. Adams-Watters, Aug 06 2009]

			a(1) = 5 because FIVE is the smallest integer whose English name is written with only straight line segments. 6 is not in the sequence because the letter S has curves. a(2) = 9 because NINE is the next integer whose English name is written with only straight line segments.

Cf. A002963, A005589.

Missing 55 and 95 added by Franklin T. Adams-Watters, Aug 06 2009

Slightly edited by Charles R Greathouse IV, Oct 05 2009

A241858 Positions of vowels in "one, two, three, four, five, six, ...".

Original entry on oeis.org

1, 3, 6, 10, 11, 13, 14, 17, 19, 21, 24, 26, 28, 29, 34, 36, 38, 40, 42, 44, 48, 51, 54, 57, 58, 61, 62, 65, 66, 69, 72, 73, 76, 79, 80, 83, 85, 88, 89, 91, 92, 96, 97, 100, 102, 104, 105, 109, 115, 119, 121, 124, 130, 133, 140, 141, 144, 149, 150, 154, 159, 161, 164, 169

Offset: 1

J. Lowell, Apr 30 2014

Consider only letters, but not spaces or punctuation.

			The letters in "four" are the twelfth through fifteenth letters in "one, two, three, four, five, six, ...". The o and u, which are 13 and 14, are vowels.

M. F. Hasler, Table of n, a(n) for n = 1..10^4

Cf. A005589, A052360.

A241858_vec(N,v=Vec("aeiou"),n,s,p,o)=vector(N,j, until( setsearch(v,s[p-o]), o+#s"@"]); p) \\ see A052360 for English(). - M. F. Hasler, Aug 11 2020

More terms from Alois P. Heinz, Apr 30 2014

a(62)-a(64) from M. F. Hasler, Aug 11 2020

A362123 Number of letters in the British English name of n, excluding spaces and hyphens.

Original entry on oeis.org

4, 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, 8, 7, 7, 9, 8, 8, 6, 9, 9, 11, 10, 10, 9, 11, 11, 10, 6, 9, 9, 11, 10, 10, 9, 11, 11, 10, 5, 8, 8, 10, 9, 9, 8, 10, 10, 9, 5, 8, 8, 10, 9, 9, 8, 10, 10, 9, 5, 8, 8, 10, 9, 9, 8, 10, 10, 9, 7, 10, 10, 12, 11, 11, 10, 12, 12, 11, 6, 9, 9, 11, 10, 10, 9, 11, 11, 10, 6, 9, 9, 11, 10, 10, 9, 11, 11, 10, 10, 16, 16, 18, 17, 17, 16, 18, 18, 17, 16, 19, 19, 21, 21, 20, 20, 22, 21, 21, 19

Offset: 0

N. J. A. Sloane, Apr 20 2023

Michael S. Branicky, Table of n, a(n) for n = 0..10000

Cf. A005589.

from num2words import num2words
def a(n): return sum(1 for c in num2words(n, lang='en_GB') if c.isalpha())
print([a(n) for n in range(121)]) # Michael S. Branicky, Apr 21 2023

More than the usual number of terms are shown in the DATA field to avoid confusion with A005589.

A030644 Decimal expansion of 10 - Pi.

Original entry on oeis.org

6, 8, 5, 8, 4, 0, 7, 3, 4, 6, 4, 1, 0, 2, 0, 6, 7, 6, 1, 5, 3, 7, 3, 5, 6, 6, 1, 6, 7, 2, 0, 4, 9, 7, 1, 1, 5, 8, 0, 2, 8, 3, 0, 6, 0, 0, 6, 2, 4, 8, 9, 4, 1, 7, 9, 0, 2, 5, 0, 5, 5, 4, 0, 7, 6, 9, 2, 1, 8, 3, 5, 9, 3, 7, 1, 3, 7, 9, 1, 0, 0, 1, 3, 7, 1, 9, 6, 5, 1, 7, 4, 6, 5, 7, 8, 8, 2, 9, 3, 2, 0, 1, 7, 8, 5

Offset: 1

Joost de Winter

			6.85840734...

Problems Drive, Eureka, 37 (1974), 8-11 and 33.

G. C. Greubel, Table of n, a(n) for n = 1..10000
Eureka, Problems Drive, 37 (1974), 8-11, 32-33, 24-27. (Annotated scanned copy)
Index entries for transcendental numbers

Cf. A000796.

RealDigits[10 - Pi, 10, 100][[1]] (* G. C. Greubel, Jul 02 2017 *)

PARI
```
10 - Pi \\ G. C. Greubel, Jul 02 2017
```

More terms from Erich Friedman

A052384 Number of letters in the n-th decimal digit of Pi (in English).

Original entry on oeis.org

3, 4, 3, 4, 4, 3, 3, 4, 5, 4, 5, 4, 5, 4, 5, 3, 5, 5, 4, 3, 3, 3, 4, 5, 5, 5, 5, 3, 5, 4, 4, 4, 3, 5, 5, 4, 3, 4, 5, 3, 3, 4, 5, 4, 4, 5, 5, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 4, 4, 4, 4, 4, 3, 5, 4, 5, 5, 3, 3, 4, 4, 3, 3, 5, 3, 3, 4, 5, 4, 4, 5, 3, 3, 5, 4, 5, 4, 5, 3, 4, 5, 4, 3, 3, 3, 5, 4, 3, 5, 4, 5, 3, 3, 4, 5

Offset: 2

Olivier Herz (olivier.herz(AT)mines.org), Mar 10 2000

Cf. A005589.

A052384 := proc(n)
    A005589(A000796(n)) ;
end proc:
seq(A052384(n),n=2..30) ; # R. J. Mathar, Jun 30 2020

a(n) = A005589(A000796(n)). - R. J. Mathar, Jun 30 2020

a(n) = A107488(n). - R. J. Mathar, Jun 30 2020

More terms from Larry Reeves (larryr(AT)acm.org), Oct 02 2000

Offset set to 2. - R. J. Mathar, Jun 30 2020

cp's OEIS Frontend

A067278 a(n) = letters(n) + a(n-1); a(0) = 0.

Views

Author

Keywords

Examples

Crossrefs

Formula

A163828 Number of straight line segments in all letters of the capitalized English name of n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Extensions

A233184 a(n) is the least number larger than the total number of letters in the English names for all terms up to and including a(n).

Views

Author

Keywords

Comments

Links

Programs

PARI

A107322 English name for number and its reverse have the same number of letters.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Python

Extensions

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.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Extensions

A163670 Numbers whose English name (excluding spaces and hyphens) is written with only straight line segments (chisel strokes).

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A241858 Positions of vowels in "one, two, three, four, five, six, ...".

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Extensions

A362123 Number of letters in the British English name of n, excluding spaces and hyphens.

Views

Author

Keywords

Links

Crossrefs

Programs

Python

Extensions

A030644 Decimal expansion of 10 - Pi.

Views

Author

Keywords