A208892 Two distinct sets of n consecutive numbers with identical corresponding prime signatures.

2, 3, 6, 7, 10, 11, 11, 12, 13, 17, 18, 19, 68, 69, 70, 71, 76, 77, 78, 79, 130, 131, 132, 133, 134, 138, 139, 140, 141, 142, 88, 89, 90, 91, 92, 93, 232, 233, 234, 235, 236, 237, 658, 659, 660, 661, 662, 663, 664, 1090, 1091, 1092, 1093, 1094, 1095, 1096

Offset: 1

Author

Matthijs Coster, Mar 03 2012

Keywords

• nonn
• tabf

Comments

The sets are chosen to minimize the larger of the two start values, so for example, (6,7) and (10,11) would be chosen over (5,6) and (13,14) since 10 is less than 13.

The sequence can be read as follows:

2, 3,

6,7, 10,11,

11,12,13, 17,18,19,

68,69,70,71, 76,77,78,79,

130,131,132,133,134, 138,139,140,141,142

88,89,90,91,92,93, 232,233,234,235,236,237

658,659,660,661,662,663,664, 1090,1091,1092,1093,1094,1095,1096

etc

Examples

			At n=4, the consecutive numbers 68, 69, 70, and 71 have the same prime signature as 76, 77, 78, and 79.  Both have the form p^2*q, p*q, p*q*r, and p, respectively.
		

Links

• Matthijs Coster, improved Sage program for computing A208892

Crossrefs

Cf. A208893, A208894.

Cf. A046523 (smallest number with same prime signature as n).