Intended for: December 27, 2012
Timetable
- First draft entered by M. F. Hasler on December 26, 2011 ✓
- Draft reviewed by Alonso del Arte on December 27, 2011 ✓
- Draft to be approved by November 27, 2012
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A151542:
Generalized pentagonal numbers:
.
-
{ 0, 12, 27, 45, 66, 90, 117, 147, 180, 216, 255, 297, 342, 390, 441, 495, 552, ... }
Originally,
pentagonal numbers are those of the form
.
Those with the “+” sign are sometimes referred to as the “second” pentagonal numbers.
The generalized pentagonal numbers
, for
through
12, form sequences
A000326,
A005449,
A045943,
A115067,
A140090,
A140091,
A059845,
A140672,
A140673,
A140674,
A140675,
A151542.
One might wonder whether it is a pure coincidence to find many “remarkable” numbers in this sequence: multiples of 11 (as 66, 297, 495, ...) and other numbers with doubled digits (117, 255 = 2 8 − 1 and its reversal 552, 441 and 882, 1116, 1200, 1377, 1566 and its “permutation” 1665, 2205, 2322, 2442, 3225, 3366, ...), the pair 147 and 741; 216 = 6 3, etc...