A167490 a(n) = smallest number whose binary run length product = n.

0, 3, 7, 12, 31, 24, 127, 48, 56, 96, 2047, 99, 8191, 384, 224, 195, 131071, 199, 524287, 387, 896, 6144, 8388607, 391, 992, 24576, 455, 1539, 536870911, 775, 2147483647, 780, 14336, 393216, 3968, 792, 137438953471, 1572864, 57344, 1548, 2199023255551, 3079

Offset

1,2

Comments

a(p) = 2^p - 1 for prime p.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Example

a(4) = 12, because 12 is the smallest number with a binary run length product of 4.
12 decimal = 1100 binary. Run lengths in binary are 2,2, and 2*2 = 4.

Prog

(PARI)
a(n)={
  my(p=if(n==1, [], my(f=factor(n)); concat(vector(#f~, i, f[i, 1]*vector(f[i, 2], j, 1)))));
  my(i=1, j=#p, b=0);
  while(i<=j, if(bittest(b, 0),
      if(p[j]>3||j==i||p[i+1]!=2, b<<=p[j]; j--, b<<=4; i+=2),
      b++; b<<=p[i]; b--; i++));
  b
} \\ Andrew Howroyd, Nov 09 2025

Crossrefs

Cf. A167489 (binary run length product).

Cf. A167491 (this sequence sorted in ascending order).

Sequence in context: A377572 A240738 A047068 * A081533 A096856 A391095

Adjacent sequences: A167487 A167488 A167489 * A167491 A167492 A167493

Keyword

nonn

Author

Andrew Weimholt, Nov 05 2009

Extensions

a(31) onward from Andrew Howroyd, Nov 09 2025

Status

approved