A208893 -id:A208893 - cp's OEIS frontend

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

Matthijs Coster, Mar 03 2012

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

			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.

Matthijs Coster, improved Sage program for computing A208892

Cf. A208893, A208894.

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

A208894 First number in larger of two distinct sets of n consecutive numbers with identical corresponding prime signatures.

Original entry on oeis.org

3, 10, 17, 76, 138, 232, 1090, 2491, 3763, 3763, 15589, 90461, 133058, 133058, 566658, 566658, 1601927, 1601927

Offset: 1

Matthijs Coster, Mar 03 2012

A208892 is the main sequence for this entry.

A208892 gives both sets, A208893 the first number in the smaller set.

a(11)-a(18) from T. D. Noe, Mar 13 2012

cp's OEIS Frontend

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

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