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A159862 Main diagonal of A159861.

%I A159862 #15 Feb 13 2023 08:58:11
%S A159862 1,1,4,29,2265,18698645,1602308616574727,
%T A159862 14017675267522095175220940844027,
%U A159862 1245902734717669791621141496863001384336371908521990690157218737
%N A159862 Main diagonal of A159861.
%C A159862 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).
%H A159862 Alois P. Heinz, <a href="/A159862/b159862.txt">Table of n, a(n) for n = 1..12</a>
%p A159862 R:= (S,m)-> iquo(S+m-1, m):
%p A159862 A:= proc(m, n) option remember; `if`(n=1, 1,
%p A159862       R(parse(cat(seq(A(m, j), j=1..n-1))), m))
%p A159862     end:
%p A159862 a:= n-> A(n,n):
%p A159862 seq(a(n), n=1..10);
%t A159862 R[S_, m_] := Quotient[S + m - 1, m];
%t A159862 A[m_, n_] := If[n == 1, 1, R[ToExpression@StringJoin[ToString /@ Table[A[m, j], {j, 1, n - 1}]], m]];
%t A159862 a[n_] := A[n, n];
%t A159862 Table[a[n], {n, 1, 10}] (* _Jean-François Alcover_, Feb 13 2023, after Maple code *)
%Y A159862 Cf. A156146, A156147, A000040, A010783.
%K A159862 easy,nonn
%O A159862 1,3
%A A159862 _Eric Angelini_ and _Alois P. Heinz_, Apr 24 2009