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A348109 Lexicographically earliest sequence S of distinct positive terms such that the first n digits of a(n)*a(n+1) are the first n digits of S. 2
1, 10, 11, 100, 1101, 10001, 11010, 100010, 110099991, 1000100001, 1100999910, 10001000010, 110099990992, 100010000100, 11009999099191, 100010000099992, 1100999909919097, 10001000009999195, 110099990991909693, 1000100000999919493, 11009999099190969296 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A self-describing sequence.

LINKS

Michael S. Branicky, Table of n, a(n) for n = 1..1001

EXAMPLE

a(1)*a(2) = 1*10 = 10 and 1 is the 1st digit of the product and S;

a(2)*a(3) = 10*11 = 110 and 1, 1 are the first 2 digits of the product and S;

a(3)*a(4) = 11*100 = 1100 and 1, 1, 0 are the first 3 digits of the product and S;

a(4)*a(5) = 100*1101 = 110100 and 1, 1, 0, 1 are the first 4 digits of the product and S;

a(5)*a(6) = 1101*10001 = 11011101 and 1, 1, 0, 1, 1 are the first 5 digits of the product and S;

a(6)*a(7) = 10001*11010 = 110111010 and 1, 1, 0, 1, 1, 1 are the first 6 digits of the product and S; etc.

PROG

(Python)

def aupton(terms):

    alst, astr, n = [1], "1", 1

    while len(alst) < terms:

        an, n = alst[-1], len(alst)

        target, pow10 = int(astr[:n]), 1

        while len(alst) == n:

            i = 0

            while i < pow10:

                q, r = divmod(target+i, an)

                if r == 0 and q not in alst:

                    alst.append(q)

                    astr += str(q)

                    break

                i += an - r

            pow10 *= 10

            target *= 10

    return alst

print(aupton(21)) # Michael S. Branicky, Jan 07 2022

CROSSREFS

Cf. A348108.

Sequence in context: A171782 A038313 A066330 * A125099 A055611 A077813

Adjacent sequences:  A348106 A348107 A348108 * A348110 A348111 A348112

KEYWORD

base,nonn

AUTHOR

Eric Angelini and Carole Dubois, Sep 30 2021

EXTENSIONS

a(15) and beyond from Michael S. Branicky, Jan 07 2022

STATUS

approved

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Last modified September 24 23:43 EDT 2022. Contains 356951 sequences. (Running on oeis4.)