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

1,3

Comments

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

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

Example

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)

Prog

(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

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.

Sequence in context: A034397 A200750 A344607 * A279818 A378360 A263614

Adjacent sequences: A325719 A325720 A325721 * A325723 A325724 A325725

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, May 16 2019

Status

approved