A325722 Start the sequence with a(1) = 1 and read the digits one by one from there. The sequence is always extended with the product d*k, d being the digit read and k the number of d digits present up to the point of the d digit taken.

1, 1, 2, 2, 4, 4, 8, 8, 16, 3, 6, 3, 12, 6, 4, 6, 18, 12, 24, 5, 24, 6, 8, 10, 16, 5, 12, 20, 30, 32, 7, 0, 8, 36, 10, 9, 14, 16, 0, 9, 0, 12, 18, 7, 0, 40, 15, 42, 10, 0, 9, 11, 24, 12, 48, 0, 18, 0, 13, 20, 14, 48, 14, 0, 28, 0, 15, 15, 32, 22, 16, 0, 0, 27, 17, 18, 24, 36, 19, 26, 40, 56, 0, 20, 64, 0, 21, 18, 28, 0, 22, 44, 48, 72

Offset: 1

Author

Eric Angelini and Carole Dubois, May 16 2019

Keywords

• base
• nonn

Comments

Every prime number > 7 appears only once and in natural order. - Davide Rotondo, Feb 08 2024

Examples

			The sequence starts with a(1) = 1.
We read this 1, see that there is only one digit 1 so far in the sequence, thus k = 1; we have then d*k = 1 and this 1 becomes a(2);
We read a(2) = 1, see that this 1 is the 2nd digit 1 so far in the sequence, thus k = 2; we have then d*k = 2 and this 2 becomes a(3);
We read a(3) = 2, see that there is only one digit 2 so far in the sequence, thus k = 1; we have then d*k = 2 and this 2 becomes a(4);
We read a(4) = 2, see that this 2 is the 2nd digit 2 so far in the sequence, thus k = 2; we have then d*k = 4 and this 4 becomes a(5);
...
We read now the first digit of a(9) = 16 and see that this 1 is the 3rd digit 1 so far in the sequence, thus k = 3; we have then d*k = 3 and this 3 becomes a(10);
We read now the second digit of a(9) = 16 and see that this 6 is the 1st digit 6 so far in the sequence, thus k = 1; we have then d*k = 6 and this 6 becomes a(11); etc.
From _Kevin Ryde_, Feb 10 2024: (Start)
Digits d from the sequence terms, their respective occurrence number k, and consequent terms a(n) = d*k, begin:
     d = 1 1 2 2 4 4 8  8  1  6  3  6  3  1  2  6  4 ...
     k = 1 2 1 2 1 2 1  2  3  1  1  2  2  4  3  3  3 ...
  d*k  = 1 2 2 4 4 8 8 16  3  6  3 12  6  4  6 18 12 ...
(End)
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..5001
• Carole Dubois, Digit-count for this sequence and two others visible in the Xref section

Crossrefs

Cf. A325721 where the same idea is developed, but with d+k instead of d*k. See also A308232 for the concatenation kd.

Cf. A322182.

Programs

PARI

digs(x) = if (x, digits(x), [0]);
countd(listd, posd, y) = my(nb=0); for (k=1, posd, if (listd[k] == y, nb++);); nb;
lista(nn) = my(list=List(1), listd=List(1), pos=1, posd=1); for (n=1, nn, my(d = digs(list[pos])); for (i=1, #d, my(y = d[i], nb = countd(listd, posd, y)); listput(list, y*nb); my(dd = digs(y*nb)); for (j=1, #dd, listput(listd, dd[j]);); posd++;); pos++;); Vec(list); \\ Michel Marcus, Feb 09 2024