A247880 For bases b = 2, 3, ..., n, let the base-b expansion of n be [c_{1,b} c_{2,b} .. c_{r_b,b}], with the most significant "digit" on the left, 0 <= c_{i,b} < b, and c_{1,b} != 0; then a(n) is the number whose base-n expansion is the sum of all those expansions, regarding the c_{i,j} as integers mod n.

2, 7, 25, 44, 75, 106, 584, 885, 1213, 1595, 2201, 2758, 3419, 4176, 66388, 84490, 106391, 131905, 162181, 196924, 236973, 282814, 348325, 409728, 478356, 573416, 662184, 759951, 868308, 987703, 33592007, 39176497, 45480263, 52570673, 60522786, 69405129

Offset: 2

Author

Talha Ali, Sep 25 2014

Keywords

• nonn
• base
• easy

Comments

The base-n expansion of a(n) is the sum of the expansions of n in bases n, n-1, ..., 3, 2, regarding all the coefficients as numbers in the range 0 to n-1.

Examples

			For n=4, we first write 4 in bases 4, 3 and 2: 10, 11, 100, whose sum is the base 4 number 121, which is 25 in base 10.
For n=6, we get 110, 20, 12, 11, 10, whose sum (as base-6 numbers) is 203_6 = 75_10, so a(6) = 75.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 2..200

Crossrefs

Cf. A247873, A247878.

Programs

PARI

a(n) = sum(b=2, n, my(d = digits(n, b)); sum(k=1, #d, d[k]*n^(#d-k));); \\ Michel Marcus, Mar 19 2015

Extensions

Definition revised by N. J. A. Sloane, Sep 27 2014

a(7)-a(37) from Lars Blomberg, Feb 28 2015