A180027 Partial sums of A100706.

1, 112, 11223, 1122334, 112233445, 11223344556, 1122334455667, 112233445566778, 11223344556677889, 1122334455667789000, 112233445566778900111, 11223344556677890011222, 1122334455667789001122333, 112233445566778900112233444, 11223344556677890011223344555, 1122334455667789001122334455666

Offset: 0

Author

Mark Dols, Aug 07 2010

Keywords

• nonn

Comments

Up to n=8 the digits of a(n) sum up to n^2.

Similar to this, A014824 (1,12,123,1234,...) is a representation of the triangular numbers; (1,1112,1112223,1112223334,...) of the pentagonal numbers;(1,11112,111122223,...) of the hexagonal numbers, and so on. A nice thing about this sequence(s) is that the (represented) value of the integer matches the partial sums of the number of digits in the sequence.

f(n) = 100*f(n-1) + A100706(n) gives a mirrored version of this sequence, and f(n) = 10*f(n-1) + A100706(n) the symmetrical version (A002477).

Crossrefs

Cf. A014824, A100706, A002477.

Programs

PARI

A100706(n) = (10^(2*n + 1) - 1)/9;
a(n) = sum(k=0, n, A100706(k)); \\ Michel Marcus, Mar 12 2023

Formula

a(n) = Sum_{k=0..n} A100706(k). - Michel Marcus, Mar 12 2023

Extensions

More terms and edited by Michel Marcus, Mar 12 2023