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

Author

Jean-Christophe Hervé, May 05 2013

Keywords

• nonn
• easy

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.

Examples

			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.
		

Links

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

Crossrefs

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

Cf. A225212, A225224 (other continuous variants).

Programs

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);
}

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 *)