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

1,1

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

Links

Table of n, a(n) for n=1..56.

Matthijs Coster, improved Sage program for computing A208892

Example

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.

Crossrefs

Cf. A208893, A208894.

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

Sequence in context: A006877 A328832 A263881 * A085397 A307414 A073439

Adjacent sequences: A208889 A208890 A208891 * A208893 A208894 A208895

Keyword

nonn,tabf

Author

Matthijs Coster, Mar 03 2012

Status

approved