A159862 Main diagonal of A159861.

1, 1, 4, 29, 2265, 18698645, 1602308616574727, 14017675267522095175220940844027, 1245902734717669791621141496863001384336371908521990690157218737

Offset: 1

Author

Eric Angelini and Alois P. Heinz, Apr 24 2009

Keywords

• easy
• nonn

Comments

The length (number of decimal digits) of a(n) may be a power of 2 and often simply doubles, when n is increased by 1. But there are many exceptions: n = 11, 12, 13 give lengths 2^8, 3*2^7, 2^9, respectively. A factor of 3 is found in the lengths of a(n) for n = 12, 112..123, 1113..1234, 11123..12345, and so on. A factor of 7 is found for n = 1112, 11112..11122, and so on. 15 is factor of the length of a(11111112).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..12

Crossrefs

Cf. A156146, A156147, A000040, A010783.

Programs

Maple

R:= (S,m)-> iquo(S+m-1, m):
A:= proc(m, n) option remember; `if`(n=1, 1,
      R(parse(cat(seq(A(m, j), j=1..n-1))), m))
    end:
a:= n-> A(n,n):
seq(a(n), n=1..10);

Mathematica

R[S_, m_] := Quotient[S + m - 1, m];
A[m_, n_] := If[n == 1, 1, R[ToExpression@StringJoin[ToString /@ Table[A[m, j], {j, 1, n - 1}]], m]];
a[n_] := A[n, n];
Table[a[n], {n, 1, 10}] (* Jean-François Alcover, Feb 13 2023, after Maple code *)