A083292 -id:A083292 - cp's OEIS frontend

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

N. J. A. Sloane, Sep 21 2006

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

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.

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.

Differs from A083292 starting at n=100.

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

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

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

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

A083291 Triangular array read by rows: T(n,k) = k*floor(n/10) + n mod 10, 0<=k<=n.

Original entry on oeis.org

0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 3, 4, 5, 6, 7, 8, 9, 10, 11

Offset: 0

Reinhard Zumkeller, Apr 23 2003

A010879(n)=T(n,0);
A076314(0)=T(0,0), A076314(n)=T(n,1) for n>0;
A028897(n)=T(n,n) for n<=1, A028897(n)=T(n,2) for n>1;
A028898(n)=T(n,n) for n<=2, A028898(n)=T(n,3) for n>2;
A028899(n)=T(n,n) for n<=3, A028899(n)=T(n,4) for n>3;
A028900(n)=T(n,n) for n<=4, A028900(n)=T(n,5) for n>4;
A028901(n)=T(n,n) for n<=5, A028901(n)=T(n,6) for n>5;
A028902(n)=T(n,n) for n<=6, A028902(n)=T(n,7) for n>6;
A028903(n)=T(n,n) for n<=7, A028903(n)=T(n,8) for n>7;
A028904(n)=T(n,n) for n<=8, A028904(n)=T(n,9) for n>8;
T(n,n) = n for n<=9, T(n,10) = n for n>9;
A083292(n) = T(n,n).

			From _Paolo Xausa_, May 22 2024: (Start)
Triangle begins:
   [0] 0;
   [1] 1, 1;
   [2] 2, 2, 2;
   [3] 3, 3, 3, 3;
   [4] 4, 4, 4, 4, 4;
   [5] 5, 5, 5, 5, 5, 5;
   [6] 6, 6, 6, 6, 6, 6, 6;
   [7] 7, 7, 7, 7, 7, 7, 7, 7;
   [8] 8, 8, 8, 8, 8, 8, 8, 8, 8;
   [9] 9, 9, 9, 9, 9, 9, 9, 9, 9, 9;
  [10] 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10;
  ... (End)

Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of the triangle, flattened).

Table[k*Floor[n/10] + Mod[n, 10], {n, 0, 10}, {k, 0, n}]//Flatten (* Paolo Xausa, May 22 2024 *)

Offset changed to 0 by Paolo Xausa, May 22 2024

cp's OEIS Frontend

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.

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