A221646 A continuous "Look and Say" sequence (without repetition, method 2).

1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 3, 2, 1, 1, 1, 3, 1, 2, 3, 1, 1, 3, 1, 1, 1, 2, 1, 3, 2, 1, 1, 3, 3, 1, 1, 2, 1, 1, 1, 3, 1, 2, 2, 1, 2, 3, 2, 1, 1, 2, 3, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 2, 1, 3, 2, 1, 1, 3, 2, 1, 2, 2

Offset

1,4

Comments

A variant of Conway's 'Look-and-Say' sequence A005150, without run cut-off. It describes at each step the preceding digits taken altogether.

There are different optional rules to build such a sequence. This method 2 does not consider already said digits.

As in the original Look-and-Say sequence, a(n) is always equal to 1, 2 or 3. The subsequence 3,3,3 never appears.

The sequence is determined by pairs of digits. Terms of even rank are counts while terms of odd rank are figures.

Links

J.-C. Hervé, Table of n, a(n) for n = 1..10000

Example

a(1) = 1, then a(2) = 1 and a(3) = 1 (one 1). Leaving out the first 1 already said, we now have two 1's, then a(4) = 2 and a(5) = 1, and then a(6) = 1, a(7) = 2, a(8) = 2, a(9) = 1, etc.

Mathematica

n = 100; a[0] = 1; see = say = 0; While[say < n - 1, c = 0; dg = a[see]; While[see <= say, If[a[see] == dg, c += 1, Break[]]; see += 1]; a[++say] = c; If[say < n - 1, a[++say] = dg]]; Array[a, n, 0] (* Jean-François Alcover, Jul 11 2013, translated and adapted from J.-C. Hervé's C program *)

Prog

(C) /* computes first n terms in array a[] */
int *swys(int n) {
int a[n] ;
int see, say, c ;
a[0] = 1;
see = say = 0 ;
while( say < n-1 ) {
  c = 0 ;     /* count */
  dg = a[see] /* digit */
  while (see <= say) {
      if (a[see]== dg)  c += 1 ;
      else break ;
      see += 1 ;
      }
  a[++say] = c ;
  if (say < n-1) a[++say] = dg ;
  }
return(a);
}

Crossrefs

Cf. A005150 (original look-and-say sequence).

Cf. A225212, A225224 (other continuous variants).

Sequence in context: A183953 A080236 A351450 * A344320 A249161 A025142

Adjacent sequences: A221643 A221644 A221645 * A221647 A221648 A221649

Keyword

nonn,easy

Author

Jean-Christophe Hervé, May 05 2013

Status

approved