Richard Hoshino called
astonishing those number
whose representation can be decomposed into two parts,
and
,
such that
is equal to the sum of the integers from
to
.
Here we relax a little the requirement and also consider astonishing
if it is the sum of the integers from to .
For example, and .
Every number greater than 473 can be written as the sum of astonishing numbers.
The first astonishing numbers are
15, 27, 190, 204, 216, 429, 1353, 1863, 3078, 3388, 3591, 7119, 19900, 20328, 21252, 21762, 23287, 23490, 78403, 133533, 178623, 1301613, 200207 more terms
Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details
click here
A graph displaying how many astonishing numbers are multiples of the primes
p from 2 to 71. In black the ideal line 1/
p.