A247873 -id:A247873 - cp's OEIS frontend

A247878 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 c_{1,2} c_{2,2} ... c_{r_2,2} c_{1,3} ... c_{1,n} c_{2,n} ... c_{r_n,n}.

2, 39, 4180, 410780, 71114370, 16188759706, 35203970802248, 150323470036510005, 101010122201413121110, 82142319855341886460705, 86125744399762145472931164, 98834976539539763693131785850, 132929923088954538537350244463306, 205447801545228436007113806273864240

Offset: 2

Talha Ali, Sep 25 2014

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

			For n = 4, we first find 4 in base 2 = 1,0,0, then 4 in base 3 = 1,1, and 4 in base 4 = 1,0. The full string we now have is '1,0,0,1,1,1,0', which is the base-4 expansion of the number a(4) = 1*4^6 + 0*4^5 + 0*4^4 + 1*4^3 + 1*4^2 + 1*4^1 + 0*4^0 = 4180.

Hiroaki Yamanouchi, Table of n, a(n) for n = 2..100

Cf. A247873, A247880.

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

a(7)-a(15) from Hiroaki Yamanouchi, Oct 02 2014

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.

Original entry on oeis.org

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

Talha Ali, Sep 25 2014

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.

			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.

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

Cf. A247873, A247878.

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

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

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

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