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

2,1

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.

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A247873, A247878.

Sequence in context: A013204 A013209 A244090 * A330051 A145130 A048506

Adjacent sequences: A247877 A247878 A247879 * A247881 A247882 A247883

Keyword

nonn,base,easy

Author

Talha Ali, Sep 25 2014

Extensions

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

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

Status

approved