A370405 Lexicographically earliest sequence of distinct positive terms such that the first digit of a(n) is present in a(n+1), the first letter of the English name of a(n) is present in the English name of a(n+1) and the first letter of the French name of a(n) is present in the French name of a(n+1).

1, 14, 15, 41, 4, 24, 20, 21, 22, 23, 25, 26, 27, 28, 29, 82, 48, 34, 3, 13, 17, 117, 51, 5, 35, 30, 31, 32, 33, 36, 37, 38, 39, 43, 40, 42, 44, 45, 46, 47, 49, 54, 50, 52, 53, 55, 56, 57, 58, 59, 65, 6, 16, 61, 60, 62, 63, 64, 66, 67, 68, 69, 76, 7, 70, 71, 72, 73, 74, 75, 77, 78, 79, 87, 80, 81, 83, 84, 85

Offset

1,2

Links

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

Eric Angelini, Talking to me?, personal blog, Feb 2024.

Example

1 one=un, 14 fourteen=quatorze, 15 fifteen=quinze, 41 forty-one=quarante et un, 4 four=quatre, 24 twenty-four=vingt-quatre, 20 twenty=vingt, 21 twenty-one=vingt et un, 22 twenty-two=vingt-deux, etc.

Mathematica

a[1]=1; a[n_]:=a[n]=(k=1; While[MemberQ[Array[a, n-1], k]||FreeQ[IntegerDigits@k, First@IntegerDigits@a[n-1]]||!StringContainsQ[IntegerName[k, "Words"], First@Characters@IntegerName[a[n-1], "Words"]]||!StringContainsQ[IntegerName[k, "French"], First@Characters@IntegerName[a[n-1], "French"]], k++]; k); Array[a, 79]

Prog

(Python)
from num2words import num2words
from itertools import count, islice
def en(n): return num2words(n).replace(" and", "")
def fr(n): return num2words(n, lang='fr')
def agen(): # generator of terms
    an, aset, mink = 1, set(), 1
    while True:
        yield an
        aset.add(an)
        t1, t2, t3, k = str(an)[0], en(an)[0], fr(an)[0], mink
        an = next(k for k in count(mink) if k not in aset and t1 in str(k) and t2 in en(k) and t3 in fr(k))
        while mink in aset: mink += 1
print(list(islice(agen(), 79))) # Michael S. Branicky, Feb 18 2024

Crossrefs

Cf. A370400, A370401, A370402, A370403, A370404.

Sequence in context: A211144 A213386 A370403 * A357625 A041404 A041402

Adjacent sequences: A370402 A370403 A370404 * A370406 A370407 A370408

Keyword

base,nonn,word

Author

Eric Angelini and Giorgos Kalogeropoulos, Feb 17 2024

Status

approved