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

Author

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

Keywords

• nonn
• base

Comments

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.

Examples

			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).
		

Links

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

Programs

PARI

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}