A122618 a(n) = n_n, where "N_b" denotes "N read in base b": if N = Sum c_i 10^i then N_b = Sum c_i b^i.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 250, 256, 262, 268, 274, 280, 286, 292, 298, 304, 360, 367, 374, 381, 388

Offset: 1

Author

N. J. A. Sloane, Sep 21 2006

Keywords

• nonn
• base
• easy

Comments

The definition applies even if b < 10. Examples: 23_45 = 2*45 + 3 = 93, 23_2 = 2*2 + 3 = 7.

References

• David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 393-402.

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..10000
• David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing, arXiv:math/0611293 [math.NT], 2006-2007.
• David Applegate, Marc LeBrun, N. J. A. Sloane, Descending Dungeons, Problem 11286, Amer. Math. Monthly, 116 (2009) 466-467.

Crossrefs

Differs from A083292 starting at n=100.

Cf. A028897 (n_2), A122640 (2n_2).

Programs

Maple

A122618 := proc(n)
      local dgs;
      dgs := convert(n,base,10) ;
    add(op(i,dgs)*n^(i-1),i=1..nops(dgs)) ;
end proc: # R. J. Mathar, May 06 2019

Mathematica

f[n_] := FromDigits[ IntegerDigits@n, n]; Array[f, 64] (* Robert G. Wilson v, Sep 27 2006 *)

PARI

A122618(n,d=digits(n))=d*vectorv(#d,i,n^(#d-i)) \\ M. F. Hasler, Apr 22 2015