A248130 -id:A248130 - cp's OEIS frontend

A248128 Start with a(0)=50, then a(n) = three times the n-th digit of the sequence, for all n > 0.

50, 15, 0, 3, 15, 0, 9, 3, 15, 0, 27, 9, 3, 15, 0, 6, 21, 27, 9, 3, 15, 0, 18, 6, 3, 6, 21, 27, 9, 3, 15, 0, 3, 24, 18, 9, 18, 6, 3, 6, 21, 27, 9, 3, 15, 0, 9, 6, 12, 3, 24, 27, 3, 24, 18, 9, 18, 6, 3, 6, 21, 27, 9, 3, 15, 0, 27, 18, 3, 6, 9, 6, 12, 6, 21, 9, 6, 12, 3, 24

Offset: 0

Eric Angelini and M. F. Hasler, Oct 02 2014

The terms in between 0's in the sequence converge "from right to left" to a limiting sequence ...,18,6,3,6,21,27,9,3,15,0. This sequence is listed in A248129. Sequence A248130 lists the individual digits, starting from some 0 and going to the left (until another 0 would be reached); they are equal to A248129/3.
It seems natural to use offset 0 to have the initial term equal to a(0) and a(n) directly related to the n-th digit of the sequence.
All terms a(n) with index n>0 are divisible by 3, the sequence a(n)/3 is nothing else than the individual digits of this sequence.

			a(0)=50 by definition, a(1) = 15 = 3*5 (= 3 x the 1st digit of "50"), a(2) = 0 = 3*0 (3 x the 2nd digit of "50,15"), a(3) = 3 = 3*1 (= 3 x the 3rd digit of the sequence which is the 1st digit of a(1) and equals 1).

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

a(n,s=50,d=[])={for(i=1,n,print1(s",");d=concat(d,if(s,digits(s)));s=3*d[1];d=vecextract(d,"^1"));s}

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

A248128 Start with a(0)=50, then a(n) = three times the n-th digit of the sequence, for all n > 0.

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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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