A370403 Lexicographically earliest sequence of distinct positive integers such that the first digit of a(n) is present in a(n+1) and the first letter of the English name of a(n) is present in the English name of a(n+1).

1, 14, 15, 41, 4, 24, 2, 12, 10, 13, 16, 17, 61, 6, 26, 20, 21, 22, 23, 25, 27, 28, 29, 32, 3, 30, 31, 33, 34, 35, 36, 37, 38, 39, 43, 40, 42, 44, 45, 46, 47, 48, 49, 54, 5, 50, 51, 52, 53, 55, 56, 57, 58, 59, 65, 60, 62, 63, 64, 66, 67, 68, 69, 76, 7, 70, 71, 72, 73, 74, 75, 77, 78, 79, 87, 8, 18, 11, 19, 81, 80

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, 14 fourteen, 15 fifteen, 41 forty-one, 4 four, 24 twenty-four, 2 two, 12 twelve, 10 ten 13 thirteen, 16 sixteen, 17 seventeen, 61 sixty-one, 6 six, 60 sixty, 26 twenty-six, 20 twenty, 21 twenty-one, 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"]], k++]; k); Array[a, 81]

Prog

(Python)
from num2words import num2words
from itertools import count, islice
def name(n): return num2words(n).replace(" and", "")
def agen(): # generator of terms
    an, aset, mink = 1, set(), 1
    while True:
        yield an
        aset.add(an)
        t1, t2, k = str(an)[0], name(an)[0], mink
        an = next(k for k in count(mink) if k not in aset and t1 in str(k) and t2 in name(k))
        while mink in aset: mink += 1
print(list(islice(agen(), 82))) # Michael S. Branicky, Feb 18 2024

Crossrefs

Cf. A370400, A370401, A370402, A370404, A370405.

Sequence in context: A180328 A211144 A213386 * A370405 A357625 A041404

Adjacent sequences: A370400 A370401 A370402 * A370404 A370405 A370406

Keyword

base,nonn,word

Author

Eric Angelini and Giorgos Kalogeropoulos, Feb 17 2024

Status

approved