cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A355847 Irregular table read by rows, in which the rows list integers formed in the process in A180301, but generalized to other starting integers. A row ends when reaching a term in A180301.

Original entry on oeis.org

1, 2, 3, 12, 20, 21, 22, 200, 4, 6, 10, 12, 20, 21, 22, 200, 5, 6, 10, 12, 20, 21, 22, 200, 6, 10, 12, 20, 21, 22, 200, 7, 10, 12, 20, 21, 22, 200, 8, 9, 10, 12, 20, 21, 22, 200, 9, 10, 12, 20, 21, 22, 200, 10, 12, 20, 21, 22, 200
Offset: 1

Views

Author

Paul Duckett, Jul 18 2022

Keywords

Examples

			a(2) = 2 (a term in A180301);
a(3) = 3 (three), so a(4) = 12 (twelve).
The triangle starts:
   1:   1
   2:   2
   3:   3   12   20   21   22  200
   4:   4    6   10   12   20   21   22  200
   5:   5    6   10   12   20   21   22  200
   6:   6   10   12   20   21   22  200
   7:   7   10   12   20   21   22  200
   8:   8    9   10   12   20   21   22  200
   9:   9   10   12   20   21   22  200
  10:  10   12   20   21   22  200
  11:  11   12   20   21   22  200
  12:  12   20   21   22  200
  13:  13   20   21   22  200
  14:  14   16   20   21   22  200
  15:  15   16   20   21   22  200
  16:  16   20   21   22  200
  17:  17   20   21   22  200
  18:  18   19   20   21   22  200
  19:  19   20   21   22  200
  20:  20   21   22  200

A050445 Each prime appears later in alphabetical order (in American English) than the one before.

Original entry on oeis.org

2, 211, 223, 2003, 2027, 2203, 2221, 2000000000003, 2000000000203, 2000000002001, 2000000002003, 2000000002223, 2000000000000000000000000000000000041, 2000000000000000000000000000000000429, 2000000000000000000000000000000000653
Offset: 1

Views

Author

Michael Lugo (mlugo(AT)thelabelguy.com), Dec 23 1999

Keywords

Comments

From Michael S. Branicky, Aug 17 2022: (Start)
As in the companion sequence A050444, spaces, hypens and the word "and" are not included in the comparisons.
In extending the sequence to large numbers, the "American system" (Weisstein link), also known as the "short scale" (Wikipedia link), was used.
The highest term is a(38) = 2*10^63 + 2*10^36 + 2*10^12 + 2202 ("two vigintillion two undecillion two trillion two thousand two hundred ninety three"). See b-file and link to US English names of terms. (End)

Examples

			Prime 2 ("two") is followed in alphabetic order first by prime 211 ("two hundred eleven").

Links

Crossrefs

Cf. A050444, A180301.

Programs

  • Python
    from sympy import isprime
from num2words import num2words
def n2w(n): return num2words(n).replace(" and", "").replace(chr(44), "").replace(chr(32), "").replace("-", "")
def afind(limit, start=2):
    alst, last, t = [], start-1, start
    while t <= limit:
        target = n2w(last)
        while not isprime(t) or n2w(t) <= target:
            t += 1
            if t > limit: return alst
        last = t; alst.append(t)
    return alst
print(afind(3000)) # Michael S. Branicky, Aug 17 2022

Extensions

If you accept "vigintillion" as a name for 10^63 then there are more terms.
Offset changed, a(4) inserted and a(8) and beyond from Michael S. Branicky, Aug 17 2022

A345015 Starting with 1, the next entry is the next higher odd integer whose spelling in English comes lexicographically earlier.

Original entry on oeis.org

1, 5, 11, 81, 85, 801, 805, 811, 881, 885, 808001, 808005, 808011, 808081, 808085, 808801, 808805, 808811, 808881, 808885, 808000001, 808000005, 808000011, 808000081, 808000085, 808000801, 808000805, 808000811, 808000881, 808000885, 808808001, 808808005
Offset: 1

Views

Author

Paul Erickson, Sep 15 2021

Keywords

Comments

From Michael S. Branicky, Jan 04 2022: (Start)
The restriction to odd numbers prevents the trivial sequence 1, 4, 5, 8 noted in A180301.
US English is used, so 101 is "one hundred one".
Alphabetical order is with commas removed, but with spaces and hyphens included, e.g., 8800 ("eight thousand eight hundred") precedes 8018 ("eight thousand eighteen").
In extending the sequence to large numbers, the "American system" (Weisstein link), also known as the "short scale" (Wikipedia link), was used.
a(41) = 8000000001 ("eight billion one"). The highest term is a(80) = 8*10^9 + a(40) = 8808808885 ("eight billion eight hundred eight million eight hundred eight thousand eight hundred eighty-five"). See link to US English names of terms. (End)

Examples

			The first term 1 ("one") is preceded in lexicographic order first by odd number 5 ("five"), which is preceded by odd number 11 ("eleven"), and so on.

Links

Crossrefs

Cf. A180301.

Programs

  • Mathematica
    list = {1};
Do [ If  [ -1 ==
    AlphabeticOrder [   IntegerName [ list[[-1]] , "Words"] ,
     IntegerName [ i, "Words" ] ], AppendTo [ list, i] ], {i, 1, 10^5,
    2}];
list
  • Python
    from num2words import num2words
def n2w(n):
    return num2words(n).replace(" and", "") .replace(chr(44), "")
def afind(startfrom=1, limit=float('inf')):
    last, t = startfrom, startfrom + 1 + startfrom%2
    if startfrom%2 == 1:
        print(startfrom, end=", ")
    while t <= limit:
        target = n2w(last)
        while n2w(t) >= target:
            t += 2
            if t > limit: return
        last = t
        print(t, end=", ")
afind(limit=10**6) # Michael S. Branicky, Jan 04 2022

Formula

From Michael S. Branicky, Jan 04 2022: (Start)
a(10+i) = 808000 + a(i), for i in 1..10.
a(20+i) = 808000000 + a(i), for i in 1..20.
a(40+i) = 8000000000 + a(i), for i in 1..40. (End)

Extensions

a(11) and beyond from Michael S. Branicky, Jan 04 2022

A356024 a(n) is the next higher integer than n whose spelling in US English comes lexicographically later.

Original entry on oeis.org

2, 200, 12, 6, 6, 10, 10, 9, 10, 12, 12, 20, 20, 16, 16, 20, 20, 19, 20, 21, 22, 200, 200, 26, 26, 200, 200, 29, 200, 31, 32, 200, 200, 36, 36, 200, 200, 39, 200, 41, 42, 60, 60, 46, 46, 60, 60, 49, 60, 51, 52, 60, 60, 56, 56, 60, 60, 59, 60, 61, 62, 200, 200
Offset: 1

Views

Author

Michael S. Branicky, Jul 23 2022

Keywords

Comments

Alphabetical order is with commas removed, but with spaces included, e.g., 8800 ("eight thousand eight hundred") would precede 8018 ("eight thousand eighteen").
In extending the sequence to large numbers, the "American system" (Weisstein link), also known as the "short scale" (Wikipedia link), is used.

Examples

			a(1) = 2 since "two" is after "one".
a(2) = 200 since "two hundred" is after "two".
a(2202) = 2000000000000 since "two trillion" is after "two thousand two hundred two".

Links

Crossrefs

Cf. A180301.

Programs

  • Python
    from num2words import num2words
def n2w(n): return num2words(n).replace(" and", "").replace(chr(44), "")
def a(n):
    target, t = n2w(n), n+1
    while n2w(t) <= target: t += 1
    return t
print([a(n) for n in range(1, 64)]) # Michael S. Branicky, Jul 23 2022

Formula

a(A180301(n)) = A180301(n+1).
Showing 1-4 of 4 results.

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