A248128 -id:A248128 - cp's OEIS frontend

A248129 The limiting sequence of terms preceding the 0's in A248128.

0, 15, 3, 9, 27, 21, 6, 3, 6, 18, 9, 18, 24, 3, 27, 24, 3, 12, 6, 9, 21, 6, 12, 6, 9, 6, 3, 18, 27, 3, 6, 18, 6, 3, 18, 27, 18, 9, 24, 3, 21, 6, 9, 18, 24, 3, 18, 9, 24, 3, 21, 6, 24, 3, 27, 12, 6, 9, 3, 6, 18, 27, 24, 3, 12, 6, 9, 24, 3, 27, 12, 6, 9, 3, 6, 18, 12, 6, 9, 21

Offset: 0

M. F. Hasler, Oct 02 2014

It can be shown that the terms in between two 0's of sequence A248128 consist of some additional terms followed by the preceding chunk of terms delimited by two 0's. This means that this sequence has a limit "from right to left", equal to ...,27,3,24,18,9,18,6,3,6,21,27,9,3,15,0. The present sequence lists this limiting sequence, starting with the rightmost term.
It seems natural to take the offset equal to 0, cf formula.
By construction of A248128, all terms are divisible by 3; A248129(n) = a(n)/3 yields the n-th *digit* preceding a 0 in A248128.

Cf. A248128, A248129.

a(n) = A248128(m-n) if A248128(m) = 0 and A248128(m-k) > 0 for all 0 < k <= n.

A248130 Limiting sequence of digits preceding the 0's in A248128.

Original entry on oeis.org

0, 5, 1, 3, 9, 7, 2, 1, 2, 6, 3, 6, 8, 1, 9, 8, 1, 4, 2, 3, 7, 2, 4, 2, 3, 2, 1, 6, 9, 1, 2, 6, 2, 1, 6, 9, 6, 3, 8, 1, 7, 2, 3, 6, 8, 1, 6, 3, 8, 1, 7, 2, 8, 1, 9, 4, 2, 3, 1, 2, 6, 9, 8, 1, 4, 2, 3, 8, 1, 9, 4, 2, 3, 1, 2, 6, 4, 2, 3, 7, 2, 2, 1, 6, 9, 3, 6, 8, 1, 7, 2

Offset: 0

M. F. Hasler, Oct 02 2014

a(n) = A248129(n)/3 = d(m-n) if d(m) := the m-th digit of A248128, equals 0, and m is sufficiently large as to have no digit 0 between the (m-n)th and the m-th digit of A248128.

A248131 Start with a(0) = 1, then a(n) = three times the n-th digit of the sequence.

Original entry on oeis.org

1, 3, 9, 27, 6, 21, 18, 6, 3, 3, 24, 18, 9, 9, 6, 12, 3, 24, 27, 27, 18, 3, 6, 9, 6, 12, 6, 21, 6, 21, 3, 24, 9, 18, 27, 18, 3, 6, 18, 6, 3, 18, 6, 3, 9, 6, 12, 27, 3, 24, 6, 21, 3, 24, 9, 18, 3, 24, 18, 9, 3, 24, 18, 9, 27, 18, 3, 6, 6, 21, 9, 6, 12, 18, 6, 3, 9, 6, 12, 27

Offset: 0

M. F. Hasler, Oct 02 2014

A (more natural?) variant of A248128, using the same rule but the smallest nontrivial initial value a(0)=1 instead of 50. However, none of the digits 0 and 5 can appear in the sequence if they don't appear in a(0), which motivates A248128(0)=50. See A248153 for a variant using multiples of 7 instead of 3.

All terms a(n) with index n>0 are divisible by 3, the sequence a(n)/3 yields exactly the individual digits of this sequence.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A248128-A248130.

Cf. A102251.

a248131 n = a248131_list !! n
a248131_list = 1 : (map (* 3) $
               concatMap (map (read . return) . show) a248131_list)
-- Reinhard Zumkeller, Oct 02 2014

a(n,s=1,d=[])={for(i=1,n,print1(s",");d=concat(d,if(s,digits(s)));s=3*d[1];d=vecextract(d,"^1"));s}

A248153 Start with a(0)=10, then a(n) = 7 times the n-th digit of the sequence.

Original entry on oeis.org

10, 7, 0, 49, 0, 28, 63, 0, 14, 56, 42, 21, 0, 7, 28, 35, 42, 28, 14, 14, 7, 0, 49, 14, 56, 21, 35, 28, 14, 14, 56, 7, 28, 7, 28, 49, 0, 28, 63, 7, 28, 35, 42, 14, 7, 21, 35, 14, 56, 7, 28, 7, 28, 35, 42, 49, 14, 56, 49, 14, 56, 28, 63, 0, 14, 56, 42, 21, 49, 14, 56, 21, 35

Offset: 0

M. F. Hasler, Oct 02 2014

This sequence was inspired by E. Angelini's post to the SeqFan list, cf. links.
a(0)=10 is the smallest possible choice to ensure that the digit 0 appears anywhere in the sequence. a(0)=1 would lead to the same sequence with the terms 0 removed.
By construction, all terms a(n), n>0, are divisible by 7, and a(n)/7 yields the sequence of digits of the (concatenated) terms of this sequence.
It is easy to show that the distance between two 0's is strictly increasing from one occurrence to the next one. Thus, the asymptotic density of terms and/or digits 0 is zero, and the sequence can never "enter a loop".

E. Angelini, Brute force density: triples and cubes, SeqFan list, Oct 01 2014

Cf. A248128, A248129, A248130, A248131.

a(n,s=10,m=7,d=[])={for(i=1,n,print1(s",");d=concat(d,if(s,digits(s)));s=m*d[1];d=vecextract(d,"^1"));s}

def aupton(nn):
    alst, astr = [10], "X10"
    for n in range(1, nn+1):
        alst.append(7 * int(astr[n]))
        astr += str(alst[-1])
    return alst
print(aupton(72)) # Michael S. Branicky, Oct 07 2021

cp's OEIS Frontend

A248129 The limiting sequence of terms preceding the 0's in A248128.

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Formula

A248130 Limiting sequence of digits preceding the 0's in A248128.

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Formula

A248131 Start with a(0) = 1, then a(n) = three times the n-th digit of the sequence.

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A248153 Start with a(0)=10, then a(n) = 7 times the n-th digit of the sequence.

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Python