A227857 -id:A227857 - cp's OEIS frontend

A231169 Triangle read by rows: T[i,j] = number of (distinct) letters which the English names of i and j have in common; j=0,...,i ; i=0,1,2,...

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

Offset: 0

M. F. Hasler, Nov 04 2013

This uses American English: no additional "and", i.e., "one hunded one", and short scale (10^9 = billion). Spaces and hyphens are ignored.
The diagonal yields the number of distinct letters in the (American) English name of the numbers (not A005589, which counts letters with multiplicity, or A052360 which even counts hyphens and spaces).
All numbers beyond 911 share at least one letter with any other number, except for 2000 and 2002 which don't share a letter with five. See A227857(n) for the number of numbers which have no letter in common with n.

			The triangle reads:
row 0: 4; ("zero" and "zero" have the 4 letters "e", "o", "r" and "z" in common)
row 1: 2, 3; ("zero" and "one" have {e,o} in common, "one" and "one" have {e,n,o} in common)
row 2: 1, 1, 3; (common(two,zero)={o}, common(two,one)={o}, common(two,two)={o,t,w})
row 3: 2, 1, 1, 4; (common(three,three)={e,h,r,t})
etc.

OEIS Index entries for sequences related to the English name of numbers

A231169(m,n,L=English/*see A052360*/,X=Vec(" -"))= #setintersect(setminus(Set(Vec(L(m))),X),Set(Vec(L(n))))

A368828 Numbers with the same number of zeros and letters O in their English name.

Original entry on oeis.org

0, 3, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 23, 25, 26, 27, 28, 29, 33, 35, 36, 37, 38, 39, 40, 53, 55, 56, 57, 58, 59, 63, 65, 66, 67, 68, 69, 73, 75, 76, 77, 78, 79, 83, 85, 86, 87, 88, 89, 93, 95, 96, 97, 98, 99, 103, 105, 106, 107, 108, 109, 110, 120, 130, 150, 160, 170, 180, 190, 203, 205, 206, 207

Offset: 1

Eric Angelini, Jan 07 2024

			0 = zerO (one 0 and one O), 3 = three (no 0 and no O), 5 = five (no 0 and no O), 6 = six (no 0 and no O), 7 = seven (no 0 and no O), etc.
1 is not in the sequence as (1 = One) is a contradiction, as are (2 = twO), (4 = fOur), (10 = ten), etc.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A227857, A368829 (French name).

Select[Range[0,207], Count[IntegerDigits[#],0] == Count[Characters[IntegerName[#]], "o"]&] (* Stefano Spezia, Jan 07 2024 *)

from num2words import num2words
def ok(n): return str(n).count('0') == num2words(n).count('o')
print([k for k in range(208) if ok(k)]) # Michael S. Branicky, Jan 07 2024

a(36)-a(38) corrected by Stefano Spezia, Jan 07 2024

A231270 Irregular table read by rows r=0,1,2..., which contain the list of numbers whose (American) English name has no letter in common with that of r.

Original entry on oeis.org

6, 50, 56, 60, 66, 6, 30, 36, 50, 56, 60, 66, 5, 6, 7, 9, 11, 500, 505, 506, 507, 509, 511, 600, 605, 606, 607, 609, 611, 700, 705, 706, 707, 709, 711, 900, 905, 906, 907, 909, 911, 6, 6000000, 6000006, 6000000000, 6000000006, 6006000000, 6006000006

Offset: 0

M. F. Hasler, Nov 06 2013

Row lengths are given in A227857. See there for links (motivation) and further discussion.

I conjecture that the table is finite and ends with row 6000000000000000000006006000006 having the entry [3], see examples and the (supposed) complete list given in the links section.

			row 0: zero => six, fifty, fifty-six, sixty, sixty-six.
row 1: one => six, thirty, thirty-six, fifty, fifty-six, sixty, sixty-six.
row 2: two => five, six, seven, nine, eleven, five hundred, five hundred five, ..., nine hundred eleven.
row 3: three => six, six million, six million six, six billion, six billion six, six billion six million, six billion six million six, six nonillion, ..., six nonillion six billion six million six.
row 4: four => six,seven,eight,nine,ten,eleven,twelve,......
row 5: five => two, two thousand, two thousand two.
Row 13 and row 15 are the first empty rows, i.e., of length 0, i.e., row 12 [4, 6] is followed by data for row 14 [6], then row 16 [4].
Most rows for larger numbers are empty, e.g. 145..199, 245..299, ..., 712..899, 912..1999. After row 2002 [5], the only nonempty rows are those listed in row 3, containing only [3].

M. F. Hasler, List of n, row(n) for all nonempty rows.

Cf. A227857, A231169.

{row(n,lang=English/*see A052360*/,LIM=999,start=0,step=1,verbose=0)=n==5 & LIM+=2000; n==3 && return(vector(15,i,6*sum(j=0,3,bittest(i,j)*10^[0,6,9,30][j+1])))/*special case: cannot be computed by "brute force*/; my(a=[],w=lang(n)); verbose&&print1(w," => "); w=Set(Vec(w)); forstep(k=start,LIM,step, setintersect( Set(Vec(lang(k))), w) || (verbose>1&&print1( lang(k)",")) || a=concat(a,k));a}

cp's OEIS Frontend

A231169 Triangle read by rows: T[i,j] = number of (distinct) letters which the English names of i and j have in common; j=0,...,i ; i=0,1,2,...

Views

Author

Keywords

Comments

Examples

Links

Programs

PARI

A368828 Numbers with the same number of zeros and letters O in their English name.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Python

Extensions

A231270 Irregular table read by rows r=0,1,2..., which contain the list of numbers whose (American) English name has no letter in common with that of r.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI