A244425 Consider the sequence of almost natural numbers (A007376) and arrange it in a table by antidiagonals; sequence gives the main diagonal.

1, 5, 1, 7, 5, 5, 7, 1, 7, 5, 1, 1, 1, 5, 1, 1, 1, 2, 2, 9, 3, 3, 7, 4, 4, 7, 5, 5, 7, 6, 6, 9, 7, 7, 3, 8, 9, 7, 8, 7, 7, 8, 0, 3, 7, 2, 8, 5, 3, 2, 2, 3, 5, 8, 2, 7, 3, 0, 8, 7, 7, 8, 0, 3, 7, 2, 8, 5, 3, 2, 2, 3, 5, 8, 2, 7, 3, 0, 8, 7, 7, 8, 0, 3, 7, 2, 8, 5, 3, 2, 2, 3, 5, 8, 2, 7, 3, 0, 8, 7, 7, 8, 0, 3, 7

Offset

1,2

Comments

The table is:

1, 2, 4, 7, 0, 1, 1, 9, 3, 2,

3, 5, 8, 1, 3, 6, 2, 2, 8, 3,

6, 9, 1, 1, 1, 0, 4, 2, 3, 9,

1, 1, 4, 7, 2, 2, 9, 4, 4, 4,

2, 1, 1, 1, 5, 3, 3, 0, 6, 5,

5, 8, 2, 2, 0, 5, 4, 4, 3, 0,

1, 2, 6, 3, 3, 1, 7, 5, 6, 8,

2, 2, 1, 6, 4, 4, 4, 1, 6, 7,

7, 3, 3, 2, 8, 5, 6, 9, 7, 8,

2, 7, 4, 4, 5, 2, 7, 7, 6, 5, ...

Links

Table of n, a(n) for n=1..105.

Formula

a(n) = A007376(A001844(n-1)). - Omar E. Pol, Jun 29 2014

Mathematica

almostNatural[n_, b_] := almostNatural[n, b] = Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; f[n_, m_] := (n + m - 2) (n + m - 1)/2 + m; Array[ almostNatural[ f[#, #], 10] &, 105] (* modified Jun 29 2014 *)

Crossrefs

Cf. A007376, A033307, A001844, A244426.

Sequence in context: A021663 A099218 A198129 * A332343 A035109 A301509

Adjacent sequences: A244422 A244423 A244424 * A244426 A244427 A244428

Keyword

nonn,base,tabl

Author

Robert G. Wilson v, Jun 27 2014

Status

approved