A240237 Concatenated digits of pyramidalized numbers: Write the decimal digits of n (a nonnegative integer) and take successive absolute differences ("pyramidalization"), then concatenate, from left to right, all the digits in each level of the pyramid, and finally concatenate those results for all levels, from the base up. The result is a(n).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 101, 110, 121, 132, 143, 154, 165, 176, 187, 198, 202, 211, 220, 231, 242, 253, 264, 275, 286, 297, 303, 312, 321, 330, 341, 352, 363, 374, 385, 396, 404, 413, 422, 431, 440, 451, 462, 473, 484, 495, 505, 514, 523, 532, 541, 550, 561, 572, 583, 594, 606, 615

Offset: 0

Author

Filipi R. de Oliveira, Apr 02 2014

Keywords

• nonn
• base
• easy

Comments

Through the so-called "pyramidalization" process a given nonnegative integer is decomposed into its digits, which are "reassembled" afterwards by concatenating each level of the pyramid (separately, from left to right) and subsequently concatenating these results, from the base to the top.

The number of digits of the resulting number is the triangular number t(d) where d is the number of digits in the original number n.

Examples

			a(1248) = 1248124121:
     1    --> 1
    1 2   --> 1.2
   1 2 4  --> 1.2.4
  1 2 4 8 --> 1.2.4.8 -->> 1248.124.12.1 --> 1248124121
		

Links

• Filipi R. de Oliveira, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A227876, which describes the pyramidalization process, and A000217 (triangular numbers). Cf. also A007908.

Formula

a(n) = n for 0 <= n <= 9;

a(n) = 10*n + |floor(n/10) - (n mod 10)| for 10 <= n <= 99.